bbl, welcome to the forum!
The 32 bit version of Win 7 will run perfectly fine on 64 bit hardware, as long as you have the correct drivers. Some components has different drivers for 32 bit OS's, even if it's the same version of Windows.
TM covered the bases quite well. I highly recommend to you that if you have 4GB or higher of RAM, go with 64 bit. If you have 4GB RAM, the 32 bit OS will only be able to use around 3.25GB of it, and out of that, at least 256MB will be used for your video card on a modern computer, leaving only 3GB for your OS & programs.
That's where the .75GB of extra RAM is missed. With 64 bit, you have all of your installed RAM, up to 16GB using Home Premium, up to 192GB in Pro/Enterprise/Ultimate.
http://www.zdnet.com/blog/hardware/max-memory-limits-for-64-bit-windows-7/4254
Of course, for most home users, 16GB is overkill, but there's many members here who has between 6 to 8GB. 4GB is considered the "sweet spot" for installed RAM for a typical home user, and in most of my usage, it covers me quite well.
However, if you have 3GB RAM or less, and your computer's installed RAM is maxed out, then the 32 bit version will do. There will be no performance increase by installing the 64 bit Win 7, in fact, if the installed RAM is less than 2GB, it's not advised to install 64 bit, period.
I feel that you'll like Windows 7 over whichever previous version of Windows that you're currently using, as long as you have a good install (correct drivers & all) on a healthy computer. I picked up on it (& 64 bit) fairly fast, and as long as you're not afraid of change, you should be OK.
If you need any assistance, always feel free to come back, there's plenty of knowledgeable Windows 7 users on board here.
Best of Luck,
Cat