I think it is a waste to not, at least on the front channel, have at least a 5" woofer. 2.5" and 3" "woofers" don't do much and make your sub work too hard.
I would piece together speakers and you can do that, and still make your $700 budget, with BIC DV and Polk Monitor.
I second the Pioneer 920 or Denon 591. However, adding a turntable to either will need an outboard pre-amp(which those are $30, all the way to a couple hundred)...some turntables can be bought with a pre-amp already on them.
Back to speakers....
BIC DV series...
DV62(1 pair, possible 2)
DV52 or DV32(if you don't want two pairs of 62)
DV52 or DV62 center
Monitor 30 (2 pairs)
Polk Center(CS 1/2/10/20...one of those 4 numbers)
BIC 1020 (better sub than anything Polk has, at the price it is)
Pretty much any combination of those speakers with either receiver will blow the doors off any "tiny satellite" 5.1 system.