As mentioned above the DSi, DSi XL, 3ds and newer lack a GBA slot/slot 2. Homebrew and certain DS flash carts (at this point you will mostly be looking for a Super DSTwo or DSTwo+, both are hard to find and expensive when you do, you might find a ISMM or iplayer though) have pretty good emulation and 3ds stuff is also quite good. There is some emulation in normal DS homebrew on normal DS flash carts but it is mostly a proof of concept affair.
No DS ever had a GBA link cable so link cable multiplayer, multiboot, GBA-Gamecube linkup will not be an option, saving that you grab a save and a copy of the ROM from whatever and use an emulator (if you only want to trade some pokemon that is one thing, if you want to play co-op Turok, mario kart or multiplayer Advance Wars that is another).
Some DS games benefit from having a certain GBA game in the GBA slot but most things there can be unlocked with cheats or saves uploaded to the internet, pokemon (as ever) is the main exception as it can fish things out from the GBA saves to allow you to trade pokemon up generations. There are a few others like all the things various megaman games can do. https://nintendo.fandom.com/wiki/List_of_Nintendo_DS_games_with_GBA_connectivity is a reasonable overview.
Unlike the GBC moving to the GBA (See Shantae, Zelda Oracles games, Towers 2 which was only recently released and Wendy: Every Witch Way, all of which have cheats/hacks to unlock and possibly sort issues with screens -- several would brighten colours to make up for the washed out original GBA screen as well as doing whatever in game perk they had) then no GBA game can tell it is on a DS and unlock some extras or anything.
What DS is best varies between people.
Most would probably say the DS lite had a brighter screen that is nicer to play things on, even the rather rare late stage original DS you could firmware hack to have more brightness levels is likely not up to par but maybe better than the early DS models. Buttons wise the DS lite ones are a bit weaker (never mind the power/reset slider thing) in terms of durability but it is not like the original is without problems (just ones more easily solved).
As far as holding one I personally like the original DS over the lite but will probably go almost anything else other than the visteon and maybe the GB micro for GBA buttons (gamecube controller with a GB player probably being the best choice that is not whatever I like on a PC). Get a nicely modded original GBA and many think that is the best option, though personally I quite like the GBA SP as a setup (and if you can get a 101 there then even better).
For the most part any shell replacements for anything are "basically the same as the original" or "noticeably worse". Maybe one day we could have something nice, or maybe you fancy your hand at playing with a 3d printer and all the rest (or maybe just soldering in a controller you like).