Okay well let's see here you've got a couple options
Hmmmm
Option 1 reciever something like a denon X4400H. You can score them for like 800 right now.
For amps I'd say a monoprice monolith x3 Klipsch are efficient so you could power the rest using the amps on the reciever. So let's say 1200 on that not sure of the price.
Right around 2000 there
For the fronts and surrounds I'd go all 7 or 5 RP 8000fs that's 4200 there or 3000 if you go just 5
Then the Klipsch ultra ceiling speakers not sure how much they run you have to contact a dealer
So that's about 8000 there give or take that leaves you only 2000 for screen and projector.
You can get an okay screen like an Elite or some of the budget ones for like 400 500.
Then say an Epson one of there budget 4k shift projectors right around 1500
That puts you at about 10 or 11000