Yep, all the AGP cards are backwards compatible. And don't sweat it, if you are limited to AGP 1X you are not missing anything!! AGP texturing is a joke and probably will never be able to compete with storing texture data in local video RAM.
I'm not going to preach which card you should get since I don't have all of them myself to compare. Over time I have had a Voodoo2 12Mb, Voodoo3 3000, Creative TNT2 Ultra, and currently a Creative GeForce DDR. If I were going to get a new card today and was looking at a budget price I would look at the Creative Labs GeForceMX DDR. It probably has respectable gaming and image quality performance. Or I would look into the Matrox G450. It probably does not perform as well as the MX in games but the image quality, 2D and 3D, is probably vastly superior, especially at resolutions of 1024x768 and above.
You will have to do your own research and make your own decision. These are simply the cards I would consider on a budget. You could look into a Radeon, I understand there are different versions but I'm not up on any of them. If I was I would be tempted to buy. Trying to keep the GF DDR in the system a while.