A 32-bit operating system can only utilize 2^32 bytes of RAM. That is, 4,294,967,296 bytes, or exactly 4GB. Even if you have 4GB in a 32-bit system, you will not be able to utilize it all. This is because all memory in the system needs to be addressed. This includes memory found on things such as video cards, as well as memory reserved for things like the PCI bus. When all is said and done, you will usually end up with 2.5-3.5GB of usable RAM out of your 4GB with a 32-bit operating system.
A 64-bit operating system can utilize 2^64 bytes of RAM. That is, 18,446,744,073,709,551,616 bytes, 17,179,869,184GB, or exactly 16EB (exabytes). However, 64-bit Vista is artificially limited to 8GB with the Home Basic version, 16GB with the Home Premium version, or 128GB with all other versions.
We typically recommend 64-bit Vista. When it was first released, there were some issues with compatibility, but now it's gotten to the point where basically anything that will work on 32-bit Vista will also work on 64-bit Vista. The exception to this is 16-bit software. However, with Windows going 32-bit with Windows 95, you will have to look at programs over 10 years old in order to find a 16-bit one.
We also typically recommend Vista Home Premium over Vista Ultimate. Unless "they" are after you and you really need hard drive encryption, Vista Ultimate doesn't really offer much over Vista Home Premium. If you are really enamored with the Vista Ultimate Extra, DreamScapes, which allows moving backgrounds, Stardock's DeskScapes
allows for the same thing on any version of Vista.