I had the same questions. Ended up getting a gaming computer and TGC 2019 and added a $250 of Amazon works amazing. Just made sure I got as many lumens as possible. You don’t need a $2k projector. I pieced my system together for under $5k.

YABER Y31 8500L Native 1920x1080P Projector, 2021 Upgraded Full HD Video Projector, ±50° 4D Keystone Correction Support 4K, Home Theater Projector Compatible with Phone,PC,TV Box,PS5 https://www.amazon.com/dp/B07XKS5PQG/ref=cm_sw_r_cp_api_glt_fabc_QDWJZZS81DVW203B0DM7