I'm new to the whole DS scene since I just got one. What all can be emulated, backed, or played on a DS using one of the one slot solutions mentioned?
First off, it's "Slot 1" not "one slot"

Which is nomenclature for the DS game slot vs. "Slot 2" which is for GBA games...
Using Slot 1 only devices (M3 Simply, R4, DS-X) all give you near 100% compatibility in reference to "backups" of DS roms. I say "near" because some games have issues with playing multi player games. As in they simply will not work when you try. If I understand correctly though, the compatibility is higher for multi player with the slot 1s than it is with slot 2s...
What you can't do with Slot 1 cards is play GBA roms which you could do if you were going the Slot 2 route. Most homebrew works on slot 1 cards and I'm pretty sure all homebrew works with slot 2. See SirPoonga's reply two posts above this one...
Personally, I don't really care too much about playing GBA roms because I have a GBA flash cartridge that I can play on one of my two GBA SPs or my Micro and the only homebrew I think I'll ever use is Moonshell which is compatible with slot 1. Therefor, I'll be buying an M3 Simply just as soon as my tax returns come in. Yea baby!

[edit]
Ooops, forgot to comment on emulation... Uh, no comment!

Seriously though, I don't know anything about that. Perhaps someone who does will chime in...
[/edit]