AmiNetRadio can be quite unstable, but it might be related to music formats you play. Anyway, my tries always end to crashes with it :)

I prefer Jukebox for mp3 files, because it has some more modern features.. especially the screenbar module options is what I love. You can easily control and see what's playing from other screens etc... I've so used to that now that I can't use any other programs anymore :) It's a "simple" player, but it actually has more useful options for my needs than other players.

For mods there are many options, check what MorphOS Storage has to offer for players. For example, DAPlayer looks like a solid option for a GUI based mod player (it actually plays mp3, aiff, wav, flac, ogg, CDDA raw data, midi, dbm, mod, s3m, xm, it files as well as mp3 and ogg streams and audio CDs.

MPlayer also plays mods if files are named with .mod extension. MorphOS port of MPlayer has a MUI GUI with playlists etc.