Budget GPU Recommendations; Upgrading from old GeForce 9500

Hello, I am hoping to get some advice from those with a better knowledge than I. First, let me say this, I KNOW MY PC IS A BIT OUTDATED. However, we have to settle for what we can get, and right now, this is what I have:

CPU
Intel Core 2 Quad Q8200 (4x2.3GHz)

Memory
4GB DDR2 RAM

Motherboard
G31M-SL2

Current Video Card
GeForce 9500 GT 1024MB DDR2

PSU
Mod XStream Pro 600W

Native Monitor Resolution
1360x768

Basically, I decided it was time to plan ahead and start upgrading after I got a nice deal on a new motherboard. Part of this upgrade is a new video card. I am posting current info, rather than upcoming info after the new motherboard/RAM/etc because I will not be upgrading everything all at once, so I am planning to use the current setup for a bit longer.

I am on a bit of a budget atm due to my employer graciously extending the opportunity to seek better employment elsewhere. No, I am not completely sure of the budget range atm. As such, feel free to recommend any thing better than the outdated 9500 GT that will not cost me my first born (after all, I'd hate to give up the most well behaved of the three).

I am not an avid gamer, but I do enjoy an occasional head shot or dungeon raid. Recent examples would be along the lines of COD MW3, and various older RPG's that are old enough that the GPU will not matter  

I have considered moving up to older cards that still out perform my current dinosaur, such as, the 9800 GT or the HD 4670; But I should probably get with the times and find something with a bit less wrinkles in the skin, so to speak. However, I have been out of the loop for quite some time, and I am rather unfamiliar with some of the newer to "not so old, but less than new" cards available now. This is what turns me to you all.

Thank you in advance for any advice, ideas, suggestions, etc...

-Frank