With current lenses I think the biggest difference between primes and zooms, outside of cost and lens speed, is simply a matter of personal preference. Personally, I really don't like zooms. Give me a 50/1.4 or an 85/1.4 over any zoom ever made any day of the week. But then you'll often hear people talk about how they hate the 50 and how it's the worst lens ever devised.
So what I'm getting at is that you should try and borrow or rent some lenses - both prime and zoom - and see what you like. You may like the primes, you may hate them. Only way to know for sure is to try it. And for what it's worth, a 50/1.8 from any manufacturer is generally both the sharpest and the cheapest lens available new.