$20k is a swell budget. But before buying any gear, think about what sort of performance you want to achieve.
1) Sound quality is not just the gear but the room/acoustics too. Is this a dedicated space or a family room? Either way, room treatments will help immensely. It does not have to intrude into the aesthetics if that is an issue.
2) Do you require the room to be somewhat immune to noise intrusion from other rooms? Do you desire that the AV system does not disturb other rooms? These issues may suggest taking steps to isolate the sound, and that's a totally separate matter from the acoustics.
3) How many seats do you require? 12' wide is good for 3 seats, 15' deep is very tough to fit more than one row. Especially if recliners are involved. If a second row is desired, do you plan a riser?
4) Is sound quality important beyond the main listening position (MLP)? If so, that may further impact seating locations, number/placement of surrounds, and number/placement of subwoofers. I'd suggest planning on 2 subs regardless.
5) Is the screen fixed (non-retractable)? Do you want the speakers behind it or flanking it?