For photo and video editing, you'll need as much RAM as you can get, and lots of storage space -- consider an external hard drive for archiving. You really should get a better monitor than a TV as well, since you'll be squinting at pixels all the time.
Don't bother about a built-in card reader. Just make sure you have
at least two USB slots that you can access easily, and get a USB card reader. I've got "stick" ones that work perfectly well -- basically put a card in and then treat it as a USB memory stick -- and these are very cheap. In fact, I got mine as freebies.
Speaking entirely for myself, my first stop for shopping around would be
Morgan Computers. They sell surplus, end-of-line, and refurbished computers. Their stock changes all the time, but if they have what you need, you can get a lot more computer for your money. The budget you mentioned should get you a high-powered desktop model plus a good monitor.