I think you're a little bit like me, always want to try the newest software. I understand you quite well. But which version you should choose depends on your purpose. If you are a serious Linux user for working or programming purpose, I think 12.04 LTS is better. Its features are definitely enough for learning and working, and it's LTS. But if you merely use it for fun and entertainment, then I would suggest you follow your heart, install 12.10 and 13.04 about one month later.
As with 32bit or 64bit issue, I think it's similar to LTS vs newest. Your memory is no more than 4GB, so 32bit doesn't put a significant contrain on it. Generally speaking, the most important reason people should choose 64bit is the memory is over 4GB. 64bit is not faster on everything, it's task-specific. In fact, many programmes running on a 64bit computer is infact 32bit, such as Firefox. In windows 7, both 32bit and 64 bit IE are provided by Microsoft, but what's in the taskbar as the default one is the 32bit version. Considering the possible compatiblity issue, 32bit is more robust and sometimes maybe preferred for serious work. But again, I think 64bit may be better for you.