I won't be very technical here temote, but I will say that when I obtained my laptop with Windows 7 Home Premium that I asked for a system that would allow me to perform graphic design using Adobe Photoshop, Flash as well as playing media (films, music etc) as well as doing other basic tasks. It did the job just fine for me. I think the rest pretty much depends on your system specs more than the operating system in your case. You have to be aware of what your hardware is capable of, as well as whether or not you can install a 64 bit Operating System. Last thing you want to do is screw up your system with an incompatible OS. I wanted more so I chose to upgrade, thought I'd made a mistake, and then ended up liking the fact I had upgraded (it's buried here in the forum somewhere lol). You on the other hand might not even want to.
If all you ARE doing is playing games (amongst the usual sending e-mails or word documents and tasks of lesser significance - to a gamer at least) then I would say Home Premium is your best bet. Anything beyond that seems to be more suited to small businesses and professional executives and the like who might need more practical functionality and maybe the extra added bit of security (e.g. Ultimate has bitlocker - Home Premium does not). If it's not something you really want to get at the moment because you're not sure, I would recommend looking at the Microsoft Compare Windows website
Obviously you're not looking to spend absolutely LOADS of money on a new OS disk or downloaded version, but it wouldn't hurt to go through that website to see which version of Windows you think would be best for you based on what you are most likely to do with it and whether you are likely to require any other functions that the other versions have where Home Premium does not.