Don't be afraid!
Worst-case scenario is probably that you'll just have to return the parts because they were incompatible.
But what kind of budget are we talking about here? It's difficult to recommend upgrades without knowing.
The most important thing is that you get a good video card first, though. You may indeed need more RAM, but that's secondary as far as gaming is concerned. Most medium to high-end graphics cards will outpace your other hardware, however. That being said, it's worth noting that you can easily swap out video cards in 5 minutes, meaning if you get a new PC, you won't need to buy a video card for it unless you just want to upgrade. I recommend a Radeon HD 3870; I am an ATI kind of guy though, so if you're not, you may want a 9800GT. Both are great cards for about $100 that I'm fairly confident can run those games you listed at max or nearly-max settings.
If you're not sure whether you want to go ATI or Nvidia, I'll give you a very brief rundown. Bear in mind also that I am not a technical expert on hardware, but I do have a good how cards compare in benchmarks. ATI cards are, in my experience, much better value than Nvidia. In almost every case, ATI cards are more powerful than the Nvidia cards in the same price range. However, The ATI driver, Catalyst Control Center, is not very intuitive, and gamers with ATI cards often have to use open up CCC prior to playing a game to make various changes so that the game will run optimally. It's not that much of a hassle, but if that type of thing bothers you, you may want to go with an Nvidia card, as the driver is almost unarguably better and the cards require less tweaking. If you're not much of an enthusiast, though, and don't mind slight performance and quality differences, you'll probably be able to find some satisfying settings in CCC that you won't have to adjust very much. Don't be afraid of it, either- the only setting that I ever really play with in CCC with my ATI card is the fan speed, simply because I like my PC to be very quiet if possible.
If you want to spend less, going down to the Radeon HD 3850 or 9600GT would still result in a PC that had no trouble playing games, though you may not be able to max out the settings on ArmA or Sims 3.
Whichever way you go, read some reviews of the card before you buy. You have a mini tower case, which is very small. Many medium and high-end graphics cards, in contrast, are quite large, and therefore may not fit inside your case properly, so watch out for cards with reviews that complain about their size. Just something to watch out for; again, don't let that scare you, you can always just return it.
As far as RAM, yeah, you'll probably need an upgrade there, too. RAM is the easiest thing to upgrade ever though. Just make sure whatever RAM you buy is dual-channel DDR2. If you can, go ahead and get a pack of 2 1GB sticks- it's pretty cheap and you'll be very satisfied. Don't buy any more than 2GB total, though, unless you plan to get a new PC soon, because Windows XP can't make use of more than 3-3.5GB (depending on whether you've got SP1 or SP2). I would discourage you from upgrading to Vista to solve this problem.
Try to buy RAM that is rated at 667MHz because this is what your system is currently using. You can also go with a higher speed if you want, but it'll be a waste of money on this computer because it will just run it at 667MHz anyways. Corsair has always seemed to me to be the most reliable brand in desktop memory. I'd highly recommend this
package, which costs just under $30.
As far as the processor, you're probably not looking at an upgrade there. While your processor is getting pretty old, it can probably still handle those games you mentioned at max settings, provided you've got the right video card and enough RAM. The reason I say don't upgrade is because you will not be able to find a better processor that fits your motherboard, so you will have to get a new board as well as processor to make that upgrade happen. And if you're going to do that extensive of an upgrade, I would recommend you just to buy a new PC entirely since you'll find the mini tower pretty confining.
Hope this helps! If you still are unsure what to do, some idea of what kind of budget you're looking at would help us help you!