We have seen here the excellent answer to the question: How would the Saturn V have differed if the first stage was also LH2/LOX? What if liquid methane would be used instead of kerosene? Would the tank for methane be smaller than a tank for LH2, but larger than a tank for kerosene?
Methane/LOX specific impulse is only slightly better than kerosene/LOX and it's about 25% less dense. In this case I think stretching the first stage would be more likely than fattening it; furthermore it might be possible to use a common-bulkhead tank instead of the separate tanks of the S-IC, (the temperature differential between liquid methane and liquid oxygen being relatively modest) so the external stage dimensions might not change much at all.
Methane wasn't popular as a rocket fuel at the time, of course, so there wouldn't be any viable candidates for engines to power the stage.