So GBA games are my thing, I'd recommend:

Golden Sun 1 & 2, obligatory RPGs, 1 leads into 2 and both are good.

Astro Omega Factor, loveletter to Tezuka, meaning you'll need to brush up on who Blackjack is for example.

Pokemon Emerald (Firered, Leafgreen, Ruby, Sapphire, Gold and Silver) are all on the system

Pokemon Mystery Dungeon Red Rescue Team, dungeon crawler with pokemons.

ATLA and Burning Earth, two small sprite games made by a studio here in aus, it's simple puzzles and the like but I like it.

Zone of the Enders - The Fist of Mars, tactics game set inside Z.O.E, unrelated but Kojima says it's canon anyway. Pretty good with a good selection of units.

Tactics Orge - the Knight of Lordis and Onimusha tactics. Both kinda like FFT and both pretty good games in their own right.

Metroid Fusion, some like some hate I like as it's a pretty good metroid on the GBA.

LOTR two towers and return of the king. Diablo clones essentially, smash orcs and get gear.

Breath of Fire 1 and 2, both ports from the SNES and both have re-translation patches which you really should get. Is a good series with memorable party characters, can't go wrong.

Summon Night - Swordcraft Story 1 and 2. First game is a dungeon crawler where you get material, forge them into weapons and summon help to help you in combat. Second is kinda like that but opens up more in that it's not just a dungeon but more varied landscapes. Very recommend. For helvetti's sake, pick Sugar, Best girl.

Yu-gi-oh, there's a few here. Sacred Cards I'd say is the best if you want a classic game where you're inserted into the game but just for dueling, Ultimate Masters 2006. This is a comprehensive game that covers the original and GX, introducing Neo-Elementals for example. You buy your decks, trade out cards and see where it goes, it's basically Legacy of the Duelist before it was that. I sunk so many hours into this. It continues on the DS with 07 and 08 as well I believe but 06 is a good place to start. Has duel puzzles as well, like needing to defeat an opponent in 1 turn with only the cards you draw. Gets you to think about card effects and the like. There's also Duel Academy if you want to actually be in the events of GX.

Cima the Enemy and Lufia the Ruins of Lore, Both kinda weird RPGS. CIMA has you rescuing people from a dungeon after a train gets stuck in a neververse, people can actually die and if everyone on the train dies, well you're really bad at the game. Lufia features a job system from memory and good interactions with the environment.

Shining Souls 1, 2 and Force. 1 and 2 plays like normal RPGs where Force turns into a party based game system from memory. Check em out.

Fire Emblem: Blazing Sword, Sacred Stones and 6. BS was the first FE in the west and it's just so good, Lyn, Eliwood and Hector are still fan favorites to this day because of how great their adventure was. Sacred stones improves the gameplay a little bit but still has alot of good characters (Joshua, Lute and Amelia for example). 6 is a prequel/sequel to 7 but didn't get released in the west I don't think. There is a patch out there somewhere for it, so grab that. All these games are hard but so worth it, the sprite work is honestly some of the best on the console, it's just so expressive.

Zoids Legacy is kinda slow for a Super Robot Wars clone but I still like it. Collect all the zoids, travel on the overworld map. Give it at least a try I'd say.

Metal Slug Advance is on here, if you're a fan of Metal Slug.

Riviera - The Promised Land, a full length RPG from Sting. A unique art style, battle mechanics and game in general. I like it. Translation is good. I think there was a Vita version as well with more content but the GBA version still works. Yggdra Union as well, one of the last games released that I think also got on the DS, card based unit game from the same creators, it's not bad. It's not Riviera though.

Sword of Mana is another good RPG, over land battles instead of needing to go to a separate screen I think. Lots of gorgeous sprite work.

Scourge Hive, totally forgotten game. Maybe you'll enjoy it. It's one of the ones I never played.

Advance Wars. Hope you like FE because that's all they're going to make for the next 15 years, after Days of Ruin on the DS the studio has forgotten about this series. Grab AW and Black Hole Rising. Both excellent games with good sprite work.

Broken Sword, Shadow of Templars. Yes someone actually ported over the first point and click game from the broken sword series, the videos are still images instead but it plays rather well I might say. If you wanna get into it with a graphical downgrade from it's PC counterpart, it's worth a shot.

Donkey Kong Countries 1, 2 and 3 are on the GBA as well, straight ports from the SNES. Worth having.

Lunar Legend is a remake of the SNES game Lunar Silver Star. It is worth playing however, as it's a classic RPG that has a decent translation by Ubisoft of all people, they translated alot of the GBA western releases so they're hit and miss sometimes. But yes, play it.

Medal of Honor Infiltrator is a top down sprite shooter borrowing a few things from metal slug. It plays alright, give it a look at. Avoid underground, there are no good first person shooters on the fugging GBA, as far as I know. Didn't have the power for it.

Sonic games, Super Ghouls and Ghosts and River City Ransom are some other good ones.

Megaman Battle Network. It's different than Megaman X for example in that you control some other guy and use selected chips in an RPG fashion to battle through. There's like 5 games in the series on the GBA I think. They reused alot of the sprite work.

The Harry potter games have varying degrees of Sprite works. Might be worth checking out.

Last one is Mazes of Fate. There is a DS copy of this but a first person dungeon crawling game on the GBA? Yes please, and this game was made in Argentina of all places. It really worth checking out.