If you spent approx $1k on source, 2k on electronics (either an integrated, or separates) and 2k on speakers, you could have a pretty great sounding system. You could probably get a better integrated in your price range than separates (unless you buy used), but your upgrade path becomes more limited; i.e., you could get a separate, better power amp, but then you are using the preamp of your integrated to run it, or vice versa.
If you don't think you would want to (or could afford to)upgrade for awhile, then the better integrated might make more sense. There are some great ones out there.
But don't cheat the rest of your gear just for the sake of more expensive speakers. There are some very fine new speakers up to 2k that you could definitely run with electronics even 3 times as costly. If you enjoy the sound of the speakers, you'll only enjoy them more as you improve what comes before them.
If you don't think you would want to (or could afford to)upgrade for awhile, then the better integrated might make more sense. There are some great ones out there.
But don't cheat the rest of your gear just for the sake of more expensive speakers. There are some very fine new speakers up to 2k that you could definitely run with electronics even 3 times as costly. If you enjoy the sound of the speakers, you'll only enjoy them more as you improve what comes before them.