What speakers are you trying to drive? Do you have one or two subs? As you probably know, speaker efficiency matters a lot.
It's true that most AVRs can't keep up with the impedance swings of woofers and do have under powered power supplies driving multiple amps, but if you have a well treated room with a sub (best to have dual matching subs), you can set the cross-over high in the AVR to take load off the AVR's amp and get great sound. I wouldn't expect a $500-700 AVR to provide "audiophile" quality, but if you invest your money in highly efficient speakers and dual subs you probably can get a very nice sounding system.
Honestly with HDMI 2.0 coming, why not buy used? You can get an older $2000+ AVR used for less money and have a good unit. I'd make sure it has Audyssey XT32 though.