Matching people looking for teachers

I need a website created that will match people with teachers. I am not sure of the exact skills ie php, html5, etc. that is needed. But i would like it to be as fancy as possible within my limited budget. The key aspect is I need to have a scheduler on there in order to have their available times shown. This will also allow the person to request the preferred time slot. The site will need profiles but dont think it will be too much more than that.