I'm not sure either . Originally I wanted a solution that avoided running speaker wire between L and R, and not have obsolete "smart" speakers in 10 years. Sonos and other multi-room systems promise they can do that, but you'd need two amps/streamers to do it.
Some additional requirements have come up in the meantime, like being able to occasionally connect the TV.
Multiroom systems aren't perfect though: E.g. Sonos adds an additional 75ms of delay when doing multi-room, and some of the alternatives might not have perfect enough timesync for L/R pairing in the same room.
That means it's looking more and more like I'm getting a standard "boring" setup with wires. Something like a Sonos Amp, 2.1 amp + separate streamer/Raspberry Pi, or an AVR.
This thread has helped me a lot already, many interesting ideas and products.
If you care about occasionally hooking up to the TV, the Amazon products are out. They add about 75ms of delay unconditionally which is more than any video source can handle while maintaining lip sync. Once video comes into play you need to limit delay. If the Sonos amp has a low-latency single room mode, that's great. Otherwise you will have the same problem with it. I'm guessing they have solved that though based on HDMI input.
For your use case, at this point, I would strongly consider a used Pre/Pro with HDMI, 3x SVS SoundPath wireless, two amplifiers, and two good speakers.
UMC-200 (or similar used) $200
SoundPath Wirelessx3 = $300
MA500 monoblock amplifier x2 (used) = $250
SVS SB1000 subwoofer = $450
JBL 530 "bookshelf" speakers = $250
AppleTV used = $20
You are right at budget and are pretty future-proof.
If you are willing to run wires, you can do slightly better because you don't have to pay for the wireless transmitters.
Used Denon AVR (X3500H) $500 (Also cheaper options)
Roll of Speaker Wire $50
SVS SB1000 subwoofer = $450
Subwoofer cable $25
JBL 530 "bookshelf" speakers = $250
AppleTV used = $20
If you are scared of used, get the Denon S650H on sale for $339
The second you talk about adding a TV, you want an AVR or AVP with HDMI and digital bass management.
There are cheaper alternatives to the SVS soundpath but it's the only one I found that actually posts a SINAD