FAR Part 91 is "General Flight Rules" it is basic rules and applies to all operations.
FAR 135 is the "air taxi" regulation and applies to operators of small aircraft carrying passengers or cargo for hire. Small aircraft are under 12,500 lbs, although there are exceptions above that weight, for example bizjets operate under 135
FAR 121 is the airline regs.
For a FAR 91 operator, that is private operation not for hire has no take-off weather minimums. Not to say, that is a good idea, just legally, no mins
FAR 91 is like the 600-series, and 121 and 135 like the 700-series, I believe. But US FAR 91 ops of any kind do NOT require an AOC.
GF