Hiya brian n welcome to the party,
If you knit every row and you are knitting in the round (joined into a cirlce) then yes you would get stockinette stitch, but if you are knitting back and forth (not joined but knitted flat) you would get garter stitch.
If you want garter stitch while knitting in the round you would have to knit one round and then purl one round.
And, yes, you most definetely can knit flat on circular needles, I prefer it that way anyway because the weight of the work rests either in your lap or on the cable of the circular and not on your wrists or hands. Another thing is that you won't be stuck having to run to the store to buy another set of needles to finish a project if you happen to lose half your straight set.