I play upwards of 50 GBA games a year, popping them into a GBA SP, DS, and GB Player depending on the situation (couch vs bed vs chair vs do I need screens or videos?)....
For me, the DS is probably the best overall... the image looks sharper, the battery life for GBA games is excellent, and the L/R buttons are spaced wide enough apart so I can press them frequently in comfort. In fact, I use my DS as a GBA so much that it'll still be used primarily for that purpose even when Advance Wars DS and Animal Crossing DS consume me. Course, the DS is kinda bulky....
The GB Player does let you play games on a large TV though, and it's also the means I use to grab captures. Screen quality varies... a little blurry, sometimes get weird interlacing effects.... it indeed does drop frames... and depending on the game it can become quite painful on the eyes.
Lastly, I gotta say, even though I think the DS is the best means to play GBA games, I love love love the SP... the screen may look a little washed out compared to the DS and the L/R buttons are a bit cramped, but good lord is it ever small (and those nitpicks are ever so minor anyway). I stuck a Pelican 3X battery onto my black SP, and while it did add a couple mm of size to the bottom, it's given me damn near 25 hours of play time per fill up. Combine that with the "shove it in my pocket" size and I gotta show the love. I often carry the SP in my jacket pocket with a few carts just in case (Advance Wars 2, WarioWare, and Astro Boy right now). Oh, and, the SP is relatively affordable these days. I can totally justify telling someone to get a GBA SP and 3-4 games for the same cost as a DS.
(I'm just not into the whole GBA Micro idea... on the one hand, it's the most portable and has the sharpest screen... on the other, the screen is a good 20% smaller than a regular GBA and the size makes the system a real PAIN IN THE ASS to play. Nintendo was showing the thing off with Pokemon at E3, and boy was that a mistake... not only did I get a hand cramp, but the text was illegible.)