Any Bitmap Brothers game, really. Speedball 2, The Chaos Engine, Cadaver 1&2, Gods, even Magic Pockets while you’re at it.
Then Banshee, Premiere, Bubba´n Stix and Chuck Rock 2 (!) from Core Design. My favorite Amiga-exclusive game, which for some reason barely ever (frankly never) gets mentioned in retrospective / Top 50 videos, is their excellent RPG Darkmere.
You probably know Flashback and Prince of Persia but they are worth trying again on Amiga. Wings and Stunt Car Racer are pretty cool early 3D games. Get to Turrican and Turrican 2 early so no German demands you to play it ever again. Pinball Fantasies and Pinball Dreams are also classics. Panza Kick Boxing and Benefactor are underrated. ATR, Shufflepuck Cafe and Pushover are pretty rad.
Mr Nutz, Leander, Fury of the Furries, Ruff’n Tumble, James Pond II: Codename Robocod, Fire & Ice, Myth, Unreal, Risky Woods, Elf, Elfmania and Body Blows Ultimate are the eurojank you are looking for.
You probably remember us discussing the Italian masterpiece Fightin’ Spirit on this forum. It is on a class of its own.
Batman: The Movie, Lethal Weapon and The Addams Family are interesting euro-takes on US film properties. (So is Robocop III but you need a mouse.)
Besides Banshee, Blood Money and Project X are probably the only decent euroshmups from that era? Also you have to play and discover Katakis for yourself if you are not aware of this game. Won’t spoil it. Try to get to it blind. Will be a fun surprise.
It sucks that you don’t have a mouse as the Amiga was great for adventure games, dungeon crawlers and excellent real time mousey games like Cannon Fodder, Syndicate, Worms and Lemmings (arguably the best versions of these games in many cases).