Most projectors look decent right out of the box. You can use your eyes and a calibration disc for basic black level, white level, and lens settings. The color filters are nice but you rarely need to adjust color or tint anymore. This will get you at least 80% of the way to the best your picture will ever look, maybe 90%.
If you want a picture that truly conforms to rec 709 and BT 2020 color spaces and SDR and HDR gray scales/tone mapping, you'll need to bring in a professional calibrator and pay him $500 or so for his time and expertise. I think it's well worth it for a mid range projector and up ($3000+) to get the best out of your equipment and setup. You're not going to be able to do this yourself. The measuring equipment alone is far more expensive than that, much less the expertise to use it. The results are amazing though, with custom curves and calibration settings for each signal type and projection mode. I settled on 3 modes: SDR (rec 709),SDR 2020 (SDR with wide color), and HDR.