Obviously the bigger the better. I'm aware of dvd players that will play mpeg 4 & div 4 files but not avi per se, unless they are encoded as one of the previous formats. My player plays such. Before I came to the forums I was quite ignorant of all these smaller formats. I was used to working with full quality PAL 720 x 576 which i presume for you would be NTSC which is 720 x 460 pixels.

TV series I can't really help you with other than adding HD or similar as a part of the search term. (I don't even have a digital tv as digital in my country is still relatively new .. & expensive for service or equipment.)