Genelec has fine speakers. I don't think you can go wrong with them.
If you should want to go passive, I'd suggest giving these dudes a try.
Monitors~Philharmonic Audio
They have decent drivers, great crossover design and FR profile. and are firmly within your $$ ballpark. They look easy to drive and should sound pretty sweet. (Disclosure...I have the Philharmonic 2 floorstanders and I love them.)
Ascend Sierra 1's would also be a great addition, or Nates Audio T5's, or Salk SongSurrounds. These would all be hard to beat for quality computer audio.
An inexpensive integrated amp would be all you'd need to make it all sing.
(If you need an amp when all is said and done, PM me. I have my former computer system Emotiva integrated (BPA-1) just sitting in my garage, perhaps looking for a new home.)
Good luck with your search. I really enjoy having a good computer audio system. You can see that I went a little overboard with mine...
....