There are three main components any decent - high-end gaming rig needs:
I will touch on each a bit, starting with the processor. The Semprons CPU (shorthand for processor), are actually quite fast for what you payed for it, but for better performance I'd suggest an upgrade. Before I can reccomend an upgrade, I will need to know the socket that your current CPU utilizes. I have done some quick research via google and all sources have said that your Sempron 3500+ is Socket 939. However, it could be a Socket 754 too. So please identify which socket it is, because if I don't know which socket your CPU uses, I can't reccomend a compatible CPU. For a solid, mid-ranged CPU, you will need to spend $150-200.
I'd reccomend the Athlon 64 3200+ or the Athlon 64 3700+ (leave the Athlon 64 3500+ alone!)
Also, to answer your immeadiate question, the Sempron 3500+ competes with any Celeron D CPU that is in the range of 3.4-3.6ghz.
Memory ... it's important for any good system to run fast, efficiently and can also help during gaming and multi-tasking. At the moment, 512mb is definitely a minimum, because most OS (operating systems, yours is probably Windows XP) use 300mb right off the bat, and that excludes any other applications or games. But 1Gb can really help take the strain off your computer in games and most multi-tasking situations. What makes upgrading your memory a pain in the *** is that your current setup is 2x256mb. If you wanted to upgrade and continue using the dual channel technology, then you'll need to buy 2x256mb memory sticks. The thing is, 4x256mb will run slower than 2x512mb, so I'd honestly reccomend buying 1Gb of memory (2x512mb) of Corsair value select, taking the old memory out and then popping this new stuff in. Chances are the Corsair is faster too. This shouldn't cost you anymore than $100, and the Corsair Value Select 1Gb (2x512mb) costs only $65.
Video cards, probably the most underestimated, confusing, yet important part of any gaming computer. Luckily, you have a PCI-e x16 (e stands for express) slot. This allows you to choose from any recently released video card that uses PCI-e technology. There are a ton of options, however, I will reccomend a video card that holds excellent performance for what you pay, and one that will not bottleneck (bottlenecking in computer terms means that a certain computer component cannot perform at optimal performance due to other components being to slow). Here are your best options:
eVGA 7600GT - $200
Sapphire X1800GTO (not yet released, but will be before the end of the month) - $250
The X1800GTO will most likely better than the 7600GT, but both cards are excellent performers for what you pay. You can shoot for lower end video cards, but if you can pay the extra $50 and get these cards, you will get a huge performance jump. Here are your lower-end gaming cards:
eVGA 6800GS - $150
Sapphire X1600XT - $150
Again, really try to shoot for the X1800GTO and 7600GT, you will be glad you did.
Last component that I didn't mention before, but still holds great value in your system, the PSU (Power Supply Unit).
The PSU is responsible for obviously providing enough power to your entire system. For a system like that, I'd reccomend nothing lower than a 450w PSU of a solid brand (OCZ, Antec, FSP Group Norton). This will cost you anywhere from $50-$100, depending on the brand you buy. The more expensive ones tend to be more efficient, and carry an extra fan or two to keep your case nice and cool.
I hope this helps you out. Remember, you don't have to upgrade everything, but it would be most logical because if you don't, certain components may bottleneck and therefore not be worth buying if you don't buy all those components together. This is the order in which I'd consider upgrading though in terms of priorities:
-Video Card (then you must upgrade your PSU as well)
This upgrade will cost you $400 at a minimum for everything, and shouldn't cost you more than $550-600 at the most. If you want me to post links to the brands of certain components I have reccomended just let me know. If you have any questions feel free to ask.