I also have a bit of time on both. The Cessna is typically unresponsive and more like a flying sponge (IMHO) in comparison.
Turbine, I have never been able to get a PA38 into a "flat spin". In fact, if you simply release the controls, the thing will recover by itself in 2 or 3 rotations. At least that's been my experience in over 500 hours in the thing.
I don't particularly like the PA38, but it has been misrepresented. Usually by people who've never flown it.
Haven't flown the Skipper, so I can't comment on it's good or bad points.
HLB, as far as choosing the school is concerned, go with the one you think is going to look after YOU. There are a lot of sharks out there. At your stage (pre GFPT) the type you learn on is largely irrelevant. You can worry about that around the time you start doing your Com navs.
In the meantime, try to find yourself an instructor that is dedicated, a company that has your interests at heart, and a flying program that won't milk you of your hard-earned readie$.
It's a big ask.
If you have narrowed it down to A/C types, think about going for a fly in the ones you haven't already tried. This will most likely expose you to a couple of diffferent instructor types, so you're killing 2 birds with one stone.....Then you can choose the plane and instructor to suit YOU.
Good luck.