I am a Xubuntu LTS user, considering using Debian Stable 64 bit in my next install.
When I switch to Debian, I want to go with Iceweasel, as it is packaged with the Debian package manager. I plan to use this Debian Mozilla Team wizard: http://mozilla.debian.net/.
It offers a choice of "Beta", "Aurora", "Release", and "ESR" versions of Iceweasel, but doesn't explain how those versions are different. What is the difference between these options?
As of March 10, 2016, Iceweasel has been discontinued, as reported here and elsewhere, and confirmed by the Debian Mozilla wizard. I'll leave this answer for historical information, only.
Standard Firefox and Firefox ESR 45 have been uploaded to Debian Unstable (as new source packages), and will follow the established testing route. Both will be available in all Debian distributions (Unstable, Testing, Stable, and Old Stable), via appropriate entries in the sources list.
People using Iceweasel from Debian unstable will be upgraded to Firefox ESR (a surprise, since the default Iceweasel version in both Unstable and Testing was recently based on standard Firefox, see edited original answer). Debian Stable will receive Firefox ESR after Iceweasel/Firefox ESR38 is deprecated, in about 3 months.
After posting my "recommended" answer, I realized that I didn't directly answer the question in case somebody else wanted that information. I'll do that here, starting with some context.
Edit: It appears that Debian revised its versioning of Iceweasel. I've incorporated changes below. The information reflects versions and code sources in February 2016.
Iceweasel is essentially a rebranded Firefox, although there are a few differences. It originated from a disagreement between Mozilla and Debian over use of the Firefox trademarks after Debian modifies and recompiles the Firefox source code. Other than the branding, the main difference is that Iceweasel does not include some of the third-party additions that Mozilla bundles with Firefox, such as Pocket.
There are now three versions of Iceweasel:
Iceweasel Beta is based on the beta release of Firefox. It is not intended for normal use by typical users. It is basically just to get a jump on testing. It lives in Debian Experimental (see below).
Aurora appears to no longer exist. It was based on the latest release of Firefox as a way to make that available when Iceweasel was based on Firefox ESR. It lived in Debian Experimental. However, Iceweasel based on the current standard Firefox is now available in the regular repositories.
Iceweasel (referred to as "Release" in the selection wizard), is now based on standard Firefox and is available in the Unstable and Testing repositories.
It isn't yet clear whether it's released in both simultaneously or graduates from Unstable to Testing after a brief evaluation period. It reflects the current Firefox version but it isn't yet clear how much delay there is. At the time of this edit, we are a month into Firefox 44 and Iceweasel 44 is the version in both repositories.
Iceweasel ESR is based on Firefox ESR (Extended Support Release), a version that is on a much longer major release interval than standard Firefox (currently about once per year vs. 6-8 weeks for standard Firefox). It is the Debian Stable version of Iceweasel.
As of February 2016, Iceweasel ESR is based on Firefox ESR version 38, which was the last ESR release. Version 38 was originally released in May 2015 but has been patched and received security updates as recently as January 2016. The next version of Iceweasel ESR will be version 45, associated with the next Firefox ESR, which is scheduled for release in March 2016.
Debian has five categories of "distributions" (in quotes because one isn't actually released), including three active releases.
Experimental contains packages and tools that are still being developed, and are still in the alpha testing stage. Experimental isn't a complete distribution. It is a staging/collaboration/experimental area for development, when it is known that a package has problems or may have problems.
Unstable is where active development of Debian occurs. This is where third-party software starts (or graduates from Experimental), when it hasn't been tested but doesn't carry an expectation of problems.
Testing contains packages that haven't been accepted into a "stable" release yet, but are in the queue for that. Users who want newer versions of software use this distribution, essentially contributing to the beta testing. Some other Debian family Linux distributions that want to offer newer versions of software (like Ubuntu and LMDE), are based on Debian Testing.
Stable is the latest officially released distribution of Debian.
Old Stable is the previous stable release
Although the different Iceweasel versions are associated with specific Debian distributions, they can be accessed in other Debian distributions in most cases. More-stable versions are usually available in the main repository for each Debian distribution. Less-stable versions of Iceweasel are usually available through backport repositories. "More-stable" and "less-stable" refer to the code source, it isn't meant to imply anything about quality.
The exceptions: Nobody uses Debian Unstable for the oldest, most stable software, so Iceweasel ESR is not available there. Similarly, nobody sticks with the Old Stable version of Debian if they want "experimental" software, so Iceweasel Beta is not available there.
As noted in the question, Debian has a wizard here for obtaining the Iceweasel version you want for the Debian distribution you're running (which, unfortunately, lacks any explanation of what the options mean; hence, this question and this answer). Note that the wizard does not appear to reflect the changes in versioning, so its results may be unpredictable.
This answer is now moot, as described in my second answer, since Iceweasel has been discontinued. I'll leave it just for historical information.
I completely understand your desire to confine everything to the Debian Stable repository. I migrated to Debian Stable from Ubuntu-based Mint because I encountered a lot of stuff that wasn't quite ready for prime-time. There's a problem, however, with the flip side. It takes forever for anything to get released into the Stable repository, so what's there tends to be very old.
With most software, the only problem with that is you miss some newer features. Browsers are a different story. Besides the ever-changing security threats, the associated "standards" for such things as displaying video and rendering web content are continuously evolving. If you get significantly behind the current version, you are likely to encounter problems with some web sites.
My own experience with what is offered in the Debian Stable repository is what led me to what I'm suggesting in this answer.
The Debian Stable repository currently offers both Iceweasel and Firefox ESR. Firefox ESR is designed to be a very stable product, with a long interval between major releases. The Firefox ESR offered in the Debian Stable repository appears to be an old remnant that has never been cleaned out; Debian has not offered brand-name Firefox for some time. It is Version 24.4 from March 2014 (the .4 is a security update, ESR 24 was released in September 2013). In another month (March 2016), Mozilla will be releasing Version 45 (as it happens, that also includes a new ESR version). A lot has changed on the web that gives version 24 indigestion.
The version of Iceweasel currently offered in the Stable repository is based on Firefox ESR Version 38. The initial release was in May 2015 (although there have been patches and security updates as recently as January 2016). At the time of my experience, Iceweasel was based on Firefox ESR 24.
Note that it is possible to install versions of Iceweasel based on newer versions of Firefox by accessing the repositories for other Debian releases. I posted another answer that goes into more detail on this aspect.
Both the Firefox ESR and Iceweasel available in the Stable repository caused problems for me with many web sites. At that time, both products were a little under a year past their original release dates. The problems disappeared when I loaded the current standard Firefox.
Mozilla has a rigorous quality program of their own, plus any problems you might experience with their browser would affect only the browser; it won't hose your OS. Given that, my recommendation is to install the current version of standard Firefox. I'll explain how to do that in a way that still allows you to manage the installation via the package manager.
Mint has a Debian-based version, and their repository always has the latest version of actual Firefox, in a form ready to install in Debian via the package manager. In this case, the value isn't in getting "bleeding-edge" features (there's a testing channel for people who want that, but the latest features in normal Firefox releases are stable). Rather, the benefit is that the performance in handling current web content will be more dependable.
The procedure is simply to add the LMDE (Linux Mint Debian Edition) repository to the list used by the package manager. You then install the latest Firefox through the package manager as you would anything else, and the package manager will alert you to updates, and install them for you if you want.
Use the file manager to open /etc/apt/sources.list.
There is a provision there under Other Software to add a repository. In that box, paste:
deb http://packages.linuxmint.com debian import
and close the file. Then, from the terminal:
Get the public key (paste these lines):
sudo gpg --keyserver pgp.mit.edu --recv-keys 3EE67F3D0FF405B2
sudo gpg --export 3EE67F3D0FF405B2 > 3EE67F3D0FF405B2.gpg
sudo apt-key add ./3EE67F3D0FF405B2.gpg
sudo rm ./3EE67F3D0FF405B2.gpg
Update:
sudo apt-get update
Now you can install Firefox in one of two ways. Either use another command:
apt-get install firefox
Or, use the software manager. Search on the term Firefox and the current version will be in the list.
Edit: My own problems were due to the offerings in the Debian Stable repository. At that time, I was unaware of Aurora (which appears to no longer exist), and the Testing repository offered a version of Iceweasel that was also based on an old version of Firefox ESR. The solution in this answer was the best option at the time, and somewhat the standard fix.
Having implemented it, my system automatically keeps current with the latest Firefox. There have been no problems in 18 months. I am happy with the solution and can continue to recommend it.
As described in my other answer, Debian has changed versioning of Iceweasel. A version based on the current standard Firefox is now offered in the Testing repository. Iceweasel will lack some of the third-party functions bundled with Firefox, but for people who don't use those features and would prefer not having the bloat, that could be a plus. So users of Debian Stable now have a choice of solutions.