You should look to keep the front 3 as close matching as possible, ideally 3 by the same maker, designed to work together.
The rears do a lot less work on the whole, so you can compromise and use a cheaper pair/different make, if funds are tight.
As for the sub, it's all about quality and setup, because the human ear can't hear bass tone in the same way as you can with higher notes.
The usual suspects mentioned in the sub forums are all very good, depending on your needs.
Oh and yes, pretty well any receiver will manage ok, unless you're considering something extremely exotic.
Whilst I agree with Badger to a large extent, I have also found that the weak point with most all-in-one systems is the speakers, and that good improvements can be achieved by swapping these for proper ones.
I wouldn't be too worried about mixing brands, but it would pay to listen to the fron three together to ensure they are tonally similar, as otherwise panning sounds can be a bit wierd!!