vaidas3 has a fair point. Unless you use a lot of memory consuming programs, you should be fine, but if you do want to use all 4GB of your RAM you should go with 64bit.
As you have a retailer version, you wouldn't be able to upgrade to 64bit. I'm willing to bet you've been given an OEM license (which is tied to the first computer it's installed on), so you would have to download a 64bit version of Windows and use that. If you can manage to find your license key, you can try and use that on the downloaded version.
You will have to clean install though as there is no direct upgrade from 32bit systems to 64bit systems. But as vaidas3 said above, unless you have over, let's say, 6GB RAM, there's not much of a point. On top of this, a few programs are not compatible with 64bit systems (all mine are fine though). Anyway, if you want the full comparison, take a look at the thread linked below. It should cover just about everything.
We're also going a bit off topic so I would mark this thread Solved and then start a new thread if you want to continue this discussion. Or just have a read of the thread I linked.