I'd spend more on speakers than amp to begin with. The sound quality is in the speakers rather than the electronics.
I didn't say focus on spl particularly, but rather the sensitivity spec for the speakers rather than a max wattage rating (which is more a melting point spec than anything particularly useful). I posted a $200 new speaker set based on your parameters. How do you figure the used Onkyo htib set of speakers/sub blows the other away particularly spec-wise? Of course the best way to choose speakers is to listen to them, preferably in your own room where you will use them. I'd say the Dayton set would likely sound better than the Onkyo, but I'm of course guessing as I don't have either. A higher sensitivity speaker will need less amp to get to the same place as a lower sensitivity speaker spl-wise. With a low budget, I think this is a worthy consideration. A good set of speakers and sub are just generally going to cost more than you've budgeted unless you get really lucky on the used market (and I don't mean that Onkyo htib set).
Spending $800 on a receiver may be worthwhile, if you need the feature set such offers. That JVC is more like a $75 receiver at this point in time, tho, due to it's lack of modern connectivity and handling of current audio/video codecs as well as power/distortion profile (which may be fine for your purposes, you haven't really said much about anything but an old vcr/s-video requirement). It may be able to put out 150wpc at 8 ohm but at over 2% THD (and will be more power at 6 ohm and less power at 16 ohm, that's the way that works) but at a high rate of distortion compared to other units that are spec'd with lower distortion.
Watts and impedance and voltage are of course related via Ohm's Law, but just how you view that relationship is somewhat a question....just what importance are you placing on speaker wattage ratings for example? Why did you state the receivers output at 150wpc from 6-16 ohms....you think that's constant for that whole impedance range?
Might try this article
https://www.audioholics.com/loudspeaker-design/truth-about-matching-amplifier-power, and maybe this one about subs for room volume
https://www.audioholics.com/loudspeaker-design/subwoofer-room-size. Maybe look thru various other articles here on the site, they can help a lot on the technical side of things...
https://www.audioholics.com/av-research