Projector vs TV will be a pretty big factor here, it's going to be a big part of the budget either way you go. 4k / HDR isn't quite there yet in my opinion when it comes to projection and what is available is fairly expensive.
I think the performance you get from your speakers using an outboard amplifier is worth it, but I am sure YMMV. And that said, the bad thing these days is preamp/processors are considered higher end with generally better features so you are almost better off just buying an ARV with preouts on it.
Make sure you think long and hard before buying. I have bought stuff in this hobby only to turn around and sell it within a few years because I was ready to upgrade or didn't really keep the end game in mind.
Consider shopping on Craigslist, forums, ebay and even doing DIY subs. Your money will go so much further it is totally worth it.