WinUAE does the trick and manages to set up good system defaults. There are a number of CPUs and chipsets that it emulates so it's reminiscent of setting up a PSX emulator. Normally you won't have to do anything major to play most games.
As noted there were plenty of great Amiga games. I grew up with it so I had a bunch. Shadow of the Beast was a good platformer for its time and has awesome music even to this day. The only problem was that it came from a time where games weren't meant to be walked through in a day or two like it is now...it's hard as fuck and there's no continues. BUT it was enjoyable at the time and high quality in comparison with other games. Knights of the Sky was an awesome flighy sim but it's probably hideous by today's standards. Defender of the Crown is an eternal classic that you need to pick up. If I'm not mistaken Flashback and Out of this World(Another World) initially came out on the Amiga. I still love those games and it's my favorite platform to play them on. Wings of Fury was a hoot.
There are gripes though.
1. It's hard to find the original game images (diskette images and I think they have the file extension ADF) that haven't been tampered with. Most have been hacked or have trainers from the early days of pirating and BBSs. Some games seem to require it so they're not all bad. The original protection would have you flipping through the game manual to type in the third word of the second pararaph of page 23. The hacks can bypass that so it's for the better. The trainers can give you unlimited health in Shadow of the Beast so that's cool. For rom purists it can feel a bit "dirty".
2. The Amiga is emulated down to its horrendous load times. Back then it didn't seem so bad and reading things off a diskette were undertandably slow but now it's just grueling. It wasn't a console system so games didn't just pop up. Be prepared to look at alot of loading screens.