Either the 32-bit or the 64-bit X64 version of Windows 7 (or linux) will work fine on a 64-bit PC. Most standard laptops and desktops come with windows 7 X64 nowadays, which will run nearly all 32-bit applications besides 64-bit ones. Much of the time you won't see much difference in speed. With 4GB or more RAM, if your applications want to use it, the 64-bit OS and applications should see an advantage.
Check the MS website. I believe your Windows 7 license key works for both 32-bit and 64-bit Windows 7. This is true when you buy the retail copy, as to OEM version - I do not know. You may be able to upgrade to 64-bit for free. (assuming you have a 64-bit capable processor).
You may or may not want to depending on your requirements. While 64-bit applications can use a lot more RAM (and have a larger working register set), the application code footprint and some dynamic footprint (e.g. stack size) is slightly larger. If your system has a small amount of RAM (1GB, 2GB) you may be better off sticking with the 32-bit version. If your system is capable of going to 4GB or more, then consider adding RAM and upgrading to the 64-bit OS.
A few number of applications requiring 1-2GB of RAM may run faster but typically, if the code cannot use the additional registers efficiently then it will run a tad slower on 64-bit (due to slightly larger execuitable code and larger stack requirements).
BTW I am happy using 64-bit with 4GB of RAM (at transition point between bit-ness).
Jim Dempsey