Well, you're not going to find anything new for that budget. Here's what I'm thinking:
1) The Intel Core I7-2700 is likely going to give you the best upgrade processor-wise. It's four cores and eight threads are double that of the I3-2120's two cores and four threads. The I5-2500 doesn't have hyper-threading so it's limited to four threads just like your I3-2120.
2) Find out how your current RAM is configured. You state 4GB of RAM. Is that 1x4GB, 2x2GB, or 4x1GB modules?
2a) If it's 1x4GB, see if you can find out what the model number of module is and see if you can find an identical model for sale.
2b) If it's 2x2GB, the you should consider doing the same, but with a 2x2GB kit. On the other hand, you could replace your current 2x2GB kit with a 2x4GB kit or 2x8GB kit for a total of 16GB of RAM.
2c) If it's 4x1GB, then you should consider replacement with either a 2x4GB, 4x4GB or 2x8GB RAM kit.
This all depends on your budget and what you can find.
3) The system only has a 240 watt power supply, so that's not going to be enough to power any type of gaming graphics card. You might (and I stress, "MIGHT") get away with a Geforce GT730, but personally, I wouldn't even try without first replacing the power supply. Unfortunately, finding an upgrade is going to be more than just difficult and after the CPU and RAM upgrades, you're probably at your budget limit anyway.
-Wolf sends