I would look to see if you can find the Pioneer B22 series (not the Elite) if you don't care about looks. The Polk Signature doesn't have as good of sound but much better looks -- either are about $200 / pair. Start off with two and then add a center, then rears.
https://sites.google.com/view/speakerdata/preference-ratings-graphs provides Harman preference scores and spinorama data, link to reviews, etc. for a wide variety of speakers from $100+++.
You can make any sub wireless for about $70-100, but for your budget I would look at either the elac 10" sub or wait unti