Apologies Noisey, I didn't mean to be officious. You are quite right to think of it in that way. When the engine fails, you'll have little time to sort things out and more importantly, no brainpower available to help you. Everything you do in advance is money in the bank. I posted as I did because when instructing I teach my students to prioritise in the order posted above.
Now, to your question. I fly several different types, so the cockpit layout, and to a certain extent, restart drills are different. The latter can only be catered for by reminding oneself before every flight. But as to the question of what to check, I was taught to do a round the cockpit scan, which seems to work well in theory. In practice, I've had several engine failures and not one has restarted. In two cases tha prop had stopped. On one of those, I dived off most of my height trying to restart it to no avail. I didn't bother on the other one.
What I'm trying to get at is, yes, it's, a good idea to have a plan, and yes, you must have it in place before you have to use it, but don't get too bogged down into it, the priority is to get down safely and if the aircraft is still useable afterwards, then well done you.