I don't have more time than you can shake a stick at, but here's impressions on some turbine flying, and turboprop flying:
Spool time is a big thing to be wary of. These engines won't spool up on a dime, as
mikecweb says, so anticipate adding power beforehand. On the Brasilia, I don't really move the power levers on final...I "think" rather than "move" the PLs and suddenly the airspeed is where I want it.
Park into the wind. The cooler the start, the better. (and the better your career potential) Know your start malfunctions, both gas turbine (hot, wet, hung, giggity goo) and electrical (if your airplane has them).
Propellers are not speed brakes, treat them accordingly. This probably applies more to the larger installations, but an inflight reversal on any prop-driven airplane will ruin your day. An overspeed, and an engine failure on takeoff (no autofeather/autofeather not armed/autofeather malfunction/whatever your manufacturer calls it) are unfun.
Battery starts with a weak battery are bad and possibly expensive (and possibly career limiting

). Especially if it's hot and you have high residuals from the previous shutdown. Get a power cart if you're feeling iffy about it.