Self-catered colleges tend to have the most diverse/state school student intake. These are John Snow, Josephine Butler, South, Stephenson, all of which are on the hill. Cuths' Parson field site is also self-catered. Traditionally Hill colleges are supposed to have had greater student diversity than the Bailey colleges, although the most recent intake has shown Castle to be more diverse than Collingwood geo-demographically when looking at Acorn/POLAR4 stats.
Whichever college you become part can have a significant influence on your student experience, especially in first year when you live there - so make sure you research them well and rank them according to your suitability. Durham can be classist, but my experience of it have mostly been expressed through microaggressions on my course (history) which annoyingly are harder to call out. Durham is an enriching experience, and you will meet great people and friends here from all walks of life, but discrimination is a reality here that isn't confronted enough.