We have the built-in Onan in our Fuzion toyhauler. I don't know where you heard that they vibrate the toyhauler, but you heard wrong. You can't tell ours is running unless you listen for the exhaust noise.
I can't compare portable to built-in, but a portable will certainly be much cheaper. I believe that a Onan 5500, which is what we have, will run up around $4000 if you just go out and buy one. I think the portables are around $800 or so, maybe more for the Honda's and Yamaha's. Which are the preferred brands due to reliability and noise concerns.
The choice between propane and gas would depend on how much you plan on using it. My understanding is that a propane will go through a lot of fuel if used constantly, more than a gasoline powered one would. OTOH if you don't use it much propane is much less hassle when only used occasionally.
