Numbers, numbers, numbers. I don't know if I came through clearly with that statement but knowing your numbers is number one! It's really irrelevant what you're flying because every aircraft is still just an aircraft. Now that I'm done repeating myself over and over, here are a few things you should be reviewing.
Engine temps, power settings, and time limitations are vitality important. Don't get me wrong, when flying a C-172 around this may seem like a waste of time but forming these habits early on in your career will allow you to excel later on.
You will find that flying singles, right up to the heavies, that engine temperatures become a primary instrument you will monitor in your scan. I'll throw a few examples out from both ends of the spectrum. In any piston engine a loss of oil pressure and a rising temperature is an indication of what? Wait for it...... yes, an engine failure. I don't know about you but when I'm flying a piston, my eyes are glued to those instruments. A good ear for the engine will typically give you a heads up that something is wrong.
When looking at a turbine powered aircraft, during engine start, a rapid rise in ITT (inter turbine temperature) is a possible "hot start." Now a hot start is when the temperature inside the turbine exceeds allowable limits and essentially you fried the engine. When one engine costs more than an average home, it's important to keep on top of it.
With having operated out of many bush strips, I've made knowing my power settings a top priority. Most pavement to pavement guys think they know the importance of this one, but unless you've skimmed the trees as you prayed to god to save your butt this one last time, then I don't think the real reason has sunk in. In a piston you're limited to the firewall, which in all my experience is a standard practice. I can't think of a time other than training where I took off without full power. In the turbine world, it's a whole new set of rules. You can actually go past full power into the "transient" region. Most turbines have been de-regulated to provide better fuel burn and increase the life of the engine. When things go bad though, you can exceed the red line for short periods of time without damaging the engine.
By now if you haven't noticed a trend; I'm continually discussing limitations. I've discussed the turbine to the extent that I'm going too but I wanted to mention that even in a C-206 you will have time limitations. On departure you can fly at max power for up to five minutes. At that point, your manifold must be reduced in order to prevent engine damage.
As I've said, an aircraft is an aircraft. Take a systematic approach to each one and you'll be miles ahead. As a recap, flip to the limitation section and start there. Knowing speeds and aircraft limitation along with good hands and feet will excel you through training and will allow more time to study emergencies. I didn't touch on emergencies as depending on the aircraft and company SOP (standard operating procedures) these techniques may differ.
This may seem like common sense but when something's new, you sometimes need a little direction. I hope this has helped. Fly safe and keep it rubber side down.