By Windows 7 Ultimate that you have installed now, you probably mean the RC, right? If it is the RC, you should see "build 7100" in the bottom right-hand corner of your desktop background (unless you've covered it with a gadget). The editions of Windows 7 final are, in order of most basic to most advanced: Starter, Home Premium, Professional, Ultimate/Enterprise. I think you want Home Premium. Supposing this is all correct...
You will be able to use the RC until the final ships out and even beyond. The RC will start shutting down every 2 hours on March 1, 2010, and expires on June 1, 2010. The final version of Windows 7 ships October 22nd, 2009. So there is plenty of time to go from the RC to the final.
On the final part of your question (being able to upgrade, as most people call it, from the RC to the final), there is a lot of uncertainty and argument. IMO, it is pretty well established that you can go from the RC to the final. See here. There is also some evidence that you can actually use the upgrade version of Win7 to do this, as opposed to needing a full retail version.
Please note that upgrading from the RC to the final is not officially supported or recommended, and you will have to modify the files on the upgrade disk and then burn your own. I am not sure as to the legality of such a procedure, so I recommend using a downloaded copy of Win7 from a legit source like the MS online store if you want to try this. Then you can modify it before burning the install disk, preserving your single copy and avoiding copyright infringement, etc.
To sum it up, you can probably go from the RC to the final version. It is not, however, recommended and really should be done with a downloaded copy of Win7 that is modified to allow it before being burned to a disk.
Sorry for being long-winded, but there's a lot to explain! Does that answer your question?
The Windows 7 RC will stop working on June 1, 2010. To continue using your PC, please be prepared to reinstall a prior version of Windows or the final released version of Windows 7 before the expiration date. We recommend doing a custom (clean) installation. Here are complete instructions on how to uninstall the Pre-release version of Windows 7 and revert to a previous genuine operating system.