“Would image clarity or definition be #1? Color quality? Contrast? Lifelike depth of field perspective?”
All of the above. With a modest sized dedicated basement theater, I tried to attain them all. I would add black level, high dynamic range (HDR), and ultra-high definition (UHD) content or Apple’s Dolby Vision and HDR10+.
In order to take advantage of the highest quality content in a projector based system, total light control and a dark bat cave environment is important.
I start with a JVC DLA-RS3100 4K, laser based projector, a Panamorph DCR-J1 anamorphic lens to get more light while still running the JVC at medium laser, a Stewart StudioTek 130 G4, 115” x 49” (125”) screen, and a Lumagen Radiance Pro 4242 video processor with its Automatic Aspect Ratio Detection & Selection and Dynamic Tone Mapping for HDR Content with Accurate Color Rendition to name a few features.
I also have one of if not the best JVC and Lumagen professional calibrators in the country local to me and take advantage of his expertise. I even had him calibrate my LG 77CX OLED TV while he was at it.