I second the 9550 (128-bit version only!) for around $57-67 dollars you will get very playable performance for HL2, in dx8.1
I know for sure you can get away with High settings, in 1024x768, with NO aa, and trilinear. IMO this is very playable and you wont miss out much at all, and the card only cost a bit more then the game itself.
The best thing about Half Life 2 is it's mutiple dx modes, and its great coding. To be honest, most video cards would shock you at how well they run with this game.
EXAMPLE: the fx5200 by nvidia runs 1024x768, High, High, Tri, NO AA, Simple shadows (in DX8) with very respectable framerates. This card is quite a bit slower then the 9550 in the budget spectrum, in fact, its almost Twice as slow when compared to in games such as unreal 2004. Take a look:
http://www.driverheaven.net/reviews/955055005200/ut2004.htm
Note this test is using the 64-bit version as well!
So to make a very long story short, if your staying in the budget card spectrum, the 9550 128mb (128-bit) video card is really your best option. You could get away with dx8.1 features, in High quality, 1024x768, tri, high quality shadows, and maybe even 2x aa without a problem. Now if you force dx9, you may have to turn the detail down. (this is all providing your current system is capable as well)
Good luck!