Welcome to the forum! There are many knowledgeable members here that can give you good information, and I'll just start the ball rolling.
My system consists of bookshelf speakers and a sub, and I've been happy with how it sounds for both movies and music. Of course, your tastes may be more discerning.

However, I do believe that you can combine smaller speakers with one or more subwoofers and get good musical reproduction.
One of the great things about Aperion Audio is their 30-day no-risk policy. If you decide not to keep the speakers, then you return them with absolutely no cost to you (no shipping, no restocking, no nothing). Added to that, I have yet to hear or read anything negative about their speakers, but I've both read and heard very good things about them. So, I'd say that they are worth some serious consideration. Perhaps you won't like them, but you don't need to worry about making a financial commitment.
SVS will also let you return speakers, but you will need to pay for shipping (I believe). I don't have as much knowledge of their speakers. I've read some good reviews and some lackluster reviews, but I can't remember any bad reviews. That's for their speakers. Their subwoofers get almost universal acclaim from what I've read. I own one of their PC13-Ultra subwoofers and absolutely love it. Also, my experiences with their customer service have been outstanding. I highly recommend them as a company.
I don't have any concrete knowledge of inherently wireless subs versus subs with a wireless kit, but my tendency is to think that the wireless portion will be equivalent. So, I'd recommend that you pick the sub that you want and then worry about making it wireless afterwards. There are some fantastic subs out there. My personal experiences are with a B&W ASW1000 subwoofer and the SVS PC13-Ultra. The Ultra absolutely outperforms the B&W, but it also cost more and was newer.
You can certainly get good good amplification and processing for under $3k. I use a receiver (Pioneer Elite VSX-23) as a pre/pro, and there are other people here that use dedicated pre/pros.
Anyway, those are just some thoughts to get this thread started. Again, welcome to the forum, and happy shopping!