use iDVD, its going to automate all these problems right out the window.
take your video files, bring them into iDVD, where they MAY need to be rendered into the DVD format needed (.mpg IS a DVD acceptable format but yours might not be the exact correct one)
create a menu, chapters etc
author and burn.
😀
your DVD player can just play many different kinds of burnable media.
VCD is standard on ALL dvd players, but its useless these days accept in strange situations. It uses MPEG1, whereas DVD uses MPEG2.
It can also play MP3s, but I doubt its going to give it to you visually on your TV like iTunes does. Most likely it will just give you one LOOOONG list of file names (not even ID3 tags) which is totally stupid and doesnt really lend itself well to letting you pick n choose what music you want to listen to. You cant, say, search by genre. This player will play MP3s, but not in a good fashion, its a gimmick IMO.