Pipe size should be fine. For 15 and 20A circuits, you rarely need more than a 3/4" pipe. But you may need multiple pipes. If you're putting in enough wires to fill a 3/4", you're into to 50% derating which then requires upsizing the wire which may then fill the pipe. A 1" pipe is hard to over fill for 20A circuits unless many are considered non-current carrying conductors.
As Mike said, you should be fine with 4 circuits. No upsizing required for that. A 5th circuit would put you to 10 current carrying conductors and a 50% derate on all of them. However, you could put 11 #10 THWN's in there easily if needed (1" rigid will take up to 17 #10 THWN conductors at its fill limit).
As Mike said, you should be fine with 4 circuits. No upsizing required for that. A 5th circuit would put you to 10 current carrying conductors and a 50% derate on all of them. However, you could put 11 #10 THWN's in there easily if needed (1" rigid will take up to 17 #10 THWN conductors at its fill limit).