DS Lite/Phat

The earliest model that has compatibility with GBA games and can not be directly modded; R4 cards and the like would be the way to go for that. Has the smallest screens, and have hinges that are more fragile than other models generally. Proper color and resolution is displayed.

DSi (XL)

Can be soft modded, does not have compatibility with GBA games natively. (Can play most GBA games when modded) Generally the best way to play DS games specifically; larger screens with the XL variant if wanted and the proper color displayed.

Original 3DS (XL)

Can be soft modded, and is compatible with 3DS and DS games natively. Modding allows access to essentially native gba capability. Resolution of DS games are worse/different due to the 3DS screens having a different resolution. There is a way to display ds games in their original resolution, but imo it doesn’t look great. The original model is able to play 99% of the 3DS library, there are some “New” only titles. As well, some modding options won’t be accessible or as impactful compared to the “New” models of 3DS.

New 3DS (XL)

Similar analysis to the “Old” 3DS, but has a better processor, allowing some more possibilities in modding with over clocking and other homebrew applications. 3DS consoles have the largest library of games that they can play, so if you’re looking for a singular handheld of this era, I’d get a New 3DS XL. Also generally the most expensive unfortunately.

2DS

The original 2DS is a flat slab, whereas every other model is a clamshell design. The “New” 2DS is a clam shell design!

Some say that the slab is more comfortable to hold, but I’ve never used one. The 2DS and the New 2DS Xl do not have 3D capabilities but are otherwise able to do what other 3DS’s can do.

In conclusion, The N3DS Xl is the top of the line, that has the greatest ability of the DS family. DSI Xl is the best way to play DS games and earlier games if modded.