You are right, a /boot partition is not essential. In fact, I don't think I have ever had one.
/home is where you keep your personal stuff so you generally want to have it as big as possible. / will have your base system and any software you later install. There is no specific size it needs to be relative to /home. So, given 230 - 32 = 198GB to play with, I would partition as follows:
/ 30 GB ext4
/home 160 GB ext4
swap 8 GB swap
Of course, this is just a suggestion and you can modify it to suit your needs. Unless you are thinking about a minimal install, I would give / at least 20GB to have space to grow. The recommended size of the swap partition depends on whether you want to be able to hibernate. According to Red Hat, the recommended size of swap to allow a system with 8GB of RAM to hibernate is 2 * 8 = 16GB. If you don't need hibernation, keep it at 8GB. I have 8GB of RAM on my laptop and am quite happy with my 8GB swap partition.
My suggestion also assumes that you will be using Linux as your primary OS. If you will be switching back and forth between windows and Linux, you may want to have your personal data (documents, movies, music etc) in a shared NTFS partition. In that case, make /home much smaller. Something like:
/ 30 GB ext4
/home 30 GB ext4
/data 130 GB ntfs
swap 8 GB swap
If all your personal stuff is in /data, it will be read/writable by both Linux and Windows. In fact, in this scenario, you can make /home even smaller if you wish. Most of the things that will be placed in /home will be simple text files, configuration files for your various installed programs. What can take up more space will be your browser cache files, and various other databases set up by, for example, music players and the like. This will all depend on your specific needs and usage.
Finally, yes /home and swap can be shared between distributions with no problem. / cannot, you will need to format it or use a different partition to install another distro. As for backing up, yes having your personal data in separate partitions is always a good idea. It will make your life much easier.