CPU is fine for TF2 - no need to go quad core unless you play the newest games on ultra settings, or do a lot of video rendering. Very few games (even brand new ones) utilize 4 cores....let alone 6, 12, etc.
For TF2 increase on your setup - $300 budget
1. If you have a 64 bit operating system (and if you don't, i'd suggest formatting and installing one)...i'd bump the ram up to 8GB. It's older ram, so it could actually be harder to find, therefore the price could be more for the 4GB you need. I would look on ebay personally Probably $40 to upgrade.
2. Video card : http://www.newegg.com/Product/Product.aspx?Item=N82E16814130932. Best bang for your buck - this + ram will keep you at 300 budget. You will see a very noticeable improvement from your current card. You should never drop below 100 fps even on a 32 man server on dx9. As always, make sure your powersupply can support the card. This card should future proof you for quite some time.
If you purely want to go graphics card - you can get a used 680 GTX for around $300 now on ebay. That card will play anything out there right now. Prices dropped because the 780/780ti are both out now.
If you do choose to do a CPU upgrade..i would just wait, save up and build a brand new machine entirely. Sell this one afterwards and put a little money back in your pockets.