Well, you have so many options when it comes to Gameboy. First off you have your original DMG model which all have the pea soup green screen. The issues with it are the STN LCD is blurry and requires good lighting. You can get systems that have been modded with lighting systems though. I don't know about with a mod but normally these systems have pretty good battery life but takes 4 AAs.
Next you have the MGB model, aka the Gameboy Pocket. They only take 2 AAAs and still get pretty good battery life. Advantages over the original model are it's slimmer, slightly bigger screen that is more black and white than the original's greenish screen. The screen may be less blurry, faster response time perhaps. Generally it's a step up over the original except the sound quality of the speaker isn't as good as the original. Still you need good lighting.
Here we have the CGB model, the Gameboy Color. It only takes 2 AAs and gets possibly the best battery life from a single set of batteries than any other model. Next advantage to mention is the CGB has a TFT LCD rather than STN which is much clearer and doesn't have the blurring issues of the past ones. Still requires good lighting. But it should be mentioned that the GBC has a larger screen when playing GB and CGB titles compared to the GBA and GBA SP. Remember that when using the GBA a portion of the screen is unused when in GBC mode. The resulting viewable area is a size less than that of the CGB LCD screen size. And like the MGB the speaker isn't the best quality, but really only the original DMG model had good speakers. The CGB really is great except for its lack of built in lighting. However it is possible to get one with a lighting modification. Sadly most or all use the lighting system from a butchered GBA SP model 001.
Last up are the GBA and GBA SP. As mentioned the screen size the GB/CGB games get is smaller than on the CGB. However you have a built in lighting system with the SP, the LCD is sharp and blur free. Battery life in the GBA is nearly as good as the CGB. In the GBA SP who cares, it's rechargeable. Though the time of play you get out of that rechargeable before needing to recharge is going to be less than the GBA or CGB gets out of alkaline AAs. Another advantage besides the built in lighting is of course you can play GBA games! The GBA probably has better ergonomics than the GBA SP.
My preference would be either the CGB or GBA SP. The CGB lacks a lighting system without being modded but otherwise it's pretty great. You can even install a better speaker or do modification to it to sound better, or just use the headphone jack. Just get some good light, it shouldn't that too hard! Otherwise, the GBA SP.. the main issues are the smaller screen size during GB/CGB games is kind of a drag, and the ergonomics may not be as nice as all the other models but you can probably deal with it. A huge plus for the GBA SP is it's truly portable with its flip open design which protects the LCD screen and controls. It should fit in most pockets pretty well. The CGB may fit in some pockets but you best not have anything to scratch up your screen in there.
Since your original post was about lighting problems I think you should just buy a good condition GBA SP (either version). They aren't terribly expensive. If you want to play on the big screen, you should track down a GameCube GB Player (make sure it has the DVD disc) and get a retrousb.com SNES controller adapter for the GameCube/Wii. Or if you can live without GBC, the Super Gameboy is dirt cheap.
