A flashcart is definitely the best option for compatibility. Just one thing you should know about playing GBA on a DS or 3DS is that it lacks an extension port, so any link cable functionality is out of the question. As for the screen, the DS(i) has a slightly higher resolution, so there'll be a black border around the picture, but no stretching or anything. The 3DS has a much higher resolution screen and by default it scales the image up, but not to a whole number and that makes it blurry. The 3DS does that to DS games too, but can play in the original resolution by holding Start or Select when launching a game (you would need to do this every time, but I think there's a way to make it permanent with custom firmware).

Get a psp or ps vita instead.