amd64, i386 (32bit / 64bit) - Which version to choose?

Your CPU can run both versions. Which version you install is more or less up to you, however, if your machine has at least 4GB of RAM, I would recommend installing the amd64 version. Some more insight into the differences between 32 and 64bit architectures can be found here. As for stability and availability, it seems you've already covered this in another question, so I won't go deeper. ;-)

You can get your download here. Choose 10.10, the latest version.

If you're in no hurry, you can wait about a month, then the next version (11.04 - Natty Narwhal) will be released, with significant changes to the default user interface. If you're a beginner you will save yourself some re-learning.

If you're especially patient, it may be good to wait another two weeks or so, then the worst, inevitable, bugs popping up at release will probably be fixed already, and your ride will be smoother.