mixers?????
OK, 1. Is it a POWERED mixer? If not you have to plug its output to a power amp and then to the speaker. 2. If it is a powered mixer, find the MAIN OUT outputs (should be marked L and R) and go from there to the speakers. You might need "speakon" cab...
if i by a mic what would be better to amplify it? a PA system or a mixer?
You can get a good powered mixer with speakers. there are several available at the music store. don't buy anything more than you will need. I would probably go with used equipment if this is your first system.
Condensing guitar, bass, vocals, and drums through mixer into Eon amps: good idea or bad idea?
You mean EON powered speakers? If so, then sure -that's what the mixer is for. Just make sure it's NOT a powered mixer. You connect the LINE output to the speakers. If its a stereo mixer, you hook up left and right and then you can pan.