Full disclosure I really disliked Testors acrylics and gave up on threm quickly. They are hard to get good coverage with.
I'm in the camp of always prime. I use enamel or lacquer primer because it seems to bite into the plastic a little, or at least goes on and won't come off. The difference if any between "lacquers", "enamels" and "acrylics" has gotten really blurred to me, so I tend to experiment and then go with what works. I like stynylrez as well, assume it's some sort of lacquer.
Washing parts is fine as long as you get the soap off afterwards. I don't unless it's an older kit or resin.
What IS important is to get all of your skin oil off the plastic. i used to use a product called "plastic prep" or such, recently I bought a bottle of 95% denatured ethyl alchohol and rub my model with that.
Welcome!
Bill