Re: mixer for live sound....suggestions?
I would recommend you to get the latest generation of powered speakers from jbl, yamaha, qsc or ev. Then buy a used mixer. This way you will maximise your sound quality and flexibility. Powered mixers is not in high regards by most people.
An Allen & Heath 16ch MixWiz is a respected non - powered mixer that you easily can get hold of.
Edit: I can see that your budget is not so high, but I still stand by my recommandation.