First, your 22" display is 720P and that's all it can display. If you feed it a 1080P signal, either up-converted or BluRay, it will down-convert it to 720P.
I think the reason most all displays under 40's are 720 and not 1080 is that you can't tell the difference with a screen size that small anyway. With a 22" screen I'm also wondering if you could tell the difference between 480P and 720P?
Also, your display has an up-converter in it as well so you don't really need an up-converting dvd player either. Perhaps with your screen size and budget a standard dvd player might just be the best option for you. Picture quality can vary greatly from disc to disc whether it be a standard dvd or a BluRay disc. I have some regular old dvd's that just look fantastic even on my 65" screen. On the other hand a Bluray player can offer much more than just a true 1080P picture. You also get better sound quality should you get a home theater setup sometime in the future, and some offer internet streaming of movies and radio like Pandora etc.
Speaking of dvd's, if you have a Big Lots near you they have a wide selection of dvd's for $3-$5. Titles vary by store and you're not going to find too many blockbusters but there are some excellent titles. Here a link to a thread on the Big-Lots-sale. Lots of fun
on the subject.