The typedef policy taken by the Linux kernel for C is the best. Essentially the policy is to not use typedefs unless you are creating a new type abstraction. This is useful in cases where low-level types different among architectures, but kernel users want a common type. For example u64 is given a specific type, but the underlying type might change between builds or architectures.
typedef u64 unsigned long long;
However, it is highly likely that in C++ there are different idioms using typedefs that are perfectly acceptable, however, I would get comfortable with C before C++.
Perhaps the best way to get re-oriented with C++ is to write may one-off programs that exercise a specific feature. For example, write a template, use a library in Boost, create some threads, allocate some memory. The point isn't to learn all of this stuff, the point is to see and it so you aren't gasping for air later on when it's showtime.
Here is the Linux kernel typedef standard, taken from http://git.kernel.org/?p=linux/kernel/git/stable/linux-2.6.33.y.git;a=blob_plain;f=Documentation/CodingStyle;hb=HEAD
  Chapter 5: Typedefs
Please don't use things like "vps_t".
It's a mistake to use typedef for
  structures and pointers. When you see
  a
vps_t a;
in the source, what does it mean?
In contrast, if it says
struct virtual_container *a;
you can actually tell what "a" is.
Lots of people think that typedefs
  "help readability". Not so. They are
  useful only for:
(a) totally opaque objects (where the
  typedef is actively used to hide
       what the object is).
 Example: "pte_t" etc. opaque objects that you can only access using
 the proper accessor functions.
 NOTE! Opaqueness and "accessor functions" are not good in themselves.
 The reason we have them for things like pte_t etc. is that there
 really is absolutely _zero_ portably accessible information there.
(b) Clear integer types, where the
  abstraction helps avoid confusion
       whether it is "int" or "long".
 u8/u16/u32 are perfectly fine typedefs, although they fit into
 category (d) better than here.
 NOTE! Again - there needs to be a _reason_ for this. If something is
 "unsigned long", then there's no reason to do
typedef unsigned long myflags_t;
 but if there is a clear reason for why it under certain circumstances
 might be an "unsigned int" and under other configurations might be
 "unsigned long", then by all means go ahead and use a typedef.
(c) when you use sparse to literally
  create a new type for
       type-checking.
(d) New types which are identical to
  standard C99 types, in certain
       exceptional circumstances.
 Although it would only take a short amount of time for the eyes and
 brain to become accustomed to the standard types like 'uint32_t',
 some people object to their use anyway.
 Therefore, the Linux-specific 'u8/u16/u32/u64' types and their
 signed equivalents which are identical to standard types are
 permitted -- although they are not mandatory in new code of your
 own.
 When editing existing code which already uses one or the other set
 of types, you should conform to the existing choices in that code.
(e) Types safe for use in userspace.
 In certain structures which are visible to userspace, we cannot
 require C99 types and cannot use the 'u32' form above. Thus, we
 use __u32 and similar types in all structures which are shared
 with userspace.
Maybe there are other cases too, but
  the rule should basically be to NEVER
  EVER use a typedef unless you can
  clearly match one of those rules.
In general, a pointer, or a struct
  that has elements that can reasonably
  be directly accessed should never be
  a typedef.