Pretty much every thing has been covered but something else worth considering is to make sure the throttle is wide open.
This gives the best chance of a restart in most cases as any partial blockage by carb ice ect means not enough air is getting in, also the compression is slightly less to allow the engine to turn over easier (try kicking a motorbike over with the throttle open and closed to compare).
I've had a couple of engine failures and found I seemed to have plenty of time to think ... it's much easier without an instructor scrutinising your every move believe me
I have no list but as most normally aspirating engines are pretty much the same ...
Fuel on/switch tanks ... primer locked ... pump.
Mixture.
Change air ... from cold to hot or vice versa.
Mag check.
Also worth noting that with a carb ice situation, it's actually possible to keep the engine going by gently pumping the primer! This isn't a recommended thing but it may keep the engine going while you get the ice melted.
If no joy leave everything in the best start combination with the engine windmilling until 1000 feet (or less if you're happy to) and then switch everthing off and concentrate on landing.
SS
PS. For best glide if needed... stop the prop! (but again this is getting a bit involved in most cases)
