Hello edstorgeoff, welcome to the Windows 7 Forums website!
If you buy either the retail Full version or Upgrade version of Windows 7, they both will come with both the 32 bit and 64 bit version install discs. Therefore you'll be able to install either version. Also, with the Upgrade version you CAN do a full clean (custom) install of Windows 7, many people have done it and you'll save some money.
Go to the
Windows 7 Upgrade Advisor to download and install the advisor program, it will run and tell you whether you'll need 32 bit or 64 bit versions will run on your computers.
If your desktop is 64 bit capable and since you have 2GB of RAM, I would recommend installing the 64 bit version, it utilizes the RAM better and the kernel is more secure in 64 bit.
Since your laptop is running Vista, it's probably a 64 bit capapble machine too. Just run the Windows 7 Advisor on both machines and it will tell you all you need to know.
You wil need to download the Windows 7 drivers for whichever version you decide to go with. Store the drivers on a thumb drive, external hard drive or burn them to a CD-RW and you'll be good. Be sure to do this for your printer, scanner, etc. too.