I think there's a substitute for TSP now, that isn't so strong, as in wearing gloves and all that.
I've used the Bullseye (Zinsser) 123, and been very happy with it. Since it's a bonding primer, it will adhere to your surface well, and allow the paint to adhere to it. I found it best to give it at least overnight to bond. Do a fingernail test. You shouldn't be able to scratch it. Then paint away! I like the waterbased personally.
I choose satin over flat because I usually do a faux treatment, and satin fauxs better than flat.