No, you shouldn't get any prime lenses,especially manual-focus primes. They're too much work and aren't flexible enough, won't do nearly as much as a good new AF zoom. Yeah, forget about primes. Leave them for me. My 200+ aren't enough.
More seriously: I see the role of AF zooms as the TAKING of pictures, and that of MF primes as the MAKING of pictures. (AF primes are somewhere in-between.) TAKING: documenting what's in front of you. MAKING: looking closely at what's around you.
Zooms, especially AF zooms, are very flexible. They are also never 'fast' -- there just aren't any (d)SLR zooms faster than f/2.8, and those ain't cheap. Primes are smaller, can be much faster (like down to f/1.2), offer DOF control that zooms can't.
If you like the P&S experience, stick to AF zooms. If you want to learn photography, start accumulating primes.