hi M. !
i don't think you're crazy at all! all my boys have been pt'ed by 18 mos and my daughter was at 22 mos.( i have 5 kids - 7 yrs b/t 1st and last) i use cloth diapers, it makes all the diff in the world. when they can feel wetness as a consequence of emptying their bladder/bowels, they make the association much more quickly. i also start leaving them naked when they start walking and really watch their cues and try to get them on the toilet when i know they should have to go. luckily i have all hardwood floors so any accidents are no biggie !
to answer your question, i much prefer to use a real toilet whenever possible. in our house, we permanently attach those potty seats that raise up like the toilet ring. i was always worried if we tried to go in public, they'd not use a real toilet if they were used to a potty seat. for my boys, i stand them on the rim of a public toilet and let them pee down into it. my daughter actually would do this, too, but i could only let her wear skirts and dresses when we were going out until she was big enough to sit on a reg toilet w/out falling in. i have a lil guy now who is 16 mos but very tiny - is is the size of a 3-6 month old. he also won't stand and pee, he likes to sit. so for him i have to bring a portable toilet top seat along. a nice padded ring, they sell them at target. i have a huge diaper bag and carry it in there when we go out. they also make foldable ones, but i found they were not sturdy and were likely to pinch!
pre-verbally, my kids liked to make the noises to let me know they had to go. my lil guy now hisses at me to say he has to pee and grunts for poo. i wish i'd made up a sign, too - LOL