Welcome aboard!
For a MWR, I would get the regular DVD player that hooks up to a TV, and for a CD player, get a boombox variety.
For individuals, portable ones are fine. Instead of CD players, it seems the preference is for MP3 players like the iPod. There are less expensive brands like Sandisk that you can buy. In fact, this Christmas I had a very hard time locating individual CD players, the shelves were full of the MP3 players. I think CD players are on there way to extinction.
I really hope you enjoy being an AS supporter/junkie. It has snowballed for me over the last year - I have even got to meet one of my soldiers this month when he came home for R&R and have another one coming home for R&R in February. It's very rewarding doing this, and I have met some great people, both supporters and soldiers!