Record cleaning is a good idea, even with new records. I buy a lot of used records and had gotten a bit lax recently, not cleaning them all. The shop I buy most of them from cleans most of their records (except the bargain bin stuff) with a VPI 16.5. I have one at home, and when I buy records from other sources I always clean them.
Long story short, I was listening to something I bought there with my girlfriend and it looked super clean and shiny, but was really noisy. She said "you should clean that" to which I responded "It's already been cleaned, it won't do anything". To my surprise, it was noticeably quieter after I cleaned it. Needless to say, now I'm cleaning EVERY record before I play them.
I've been using the Audio Intelligent Vinyl Solution Premium One-Step Formula No. 6. I don't do any rinsing after cleaning.
Cleaning won't fix a worn or poorly pressed record, but it can do wonders for some of the second hand (and new) records you buy.