Trouble checks are important of course, but...
...having had one real EF, and one misdiagnosed one (ie as a low time PPL I thought the engine had failed when it started making the kind of racket engines make when the exhaust manifold breaks, so pulled the throttle and glided to a landing at a not-so-far airport from 10,000 feet - DUH. Sure wish I'd done the trouble checks then) I have found out one important thing that might be worth bearing in mind as part of this fairly technical discussion:
Trouble checks aside, my experience when it all went quiet was my mind went to toast. It's panic that's the most dangerous, I reckon. Really. When the fear is on, one can forget the simplest things. While the pro's that fly every day are more likely to be highly current and not screw it up, for us PPL's or anyone who doesn't have years and years of intense experience I think it's a good habit to have a simple mnemomic that reminds you of EVERYTHING. Even airspeed control is hard to remember when it's a real engine failure. You just can't believe it - the first response is denial, and the next is likely to be intense fear, unless you're way current. And it's not a big step from controlled fear, which is OK, to panic, which is not. Panic, and you could get so tied up with your trouble checks that you forget to maintain flying airspeed, for instance, and the next thing you know you've got an EF AND a spin to deal with. (Happens all the time). Or worry about your Mayday calls/trouble checks BEFORE you find the best place - or least-worst - to land, and in the process lose the option of a perfectly good paddock cos you're pointed the wrong way, with your head down.
Personally, I use SWLFMRP as a catch-all for all aircraft. (I think Sex With Llamas From Macedonia Requires Patience, personally, but whatever you're into.)
Speed (climb to convert to altitude, or as noted above nose down if on takeoff - whatever it takes), Wind (ascertain/confirm direction), Landing (Plan it, NOW - where, how, high key, low key, all that) Fuel - NOW you switch tanks, turn pump on, off, carb heat if you've got it, Mixture - check rich, wiggle, Radio (if you're gonna crash, hopefully someone will come and get you) and Pax (briefing.)
And I remind myself about those Macedonian Llamas every time I fly. And when I'm not flying. Even when I'm driving, or riding a bike. I think the big thing is to not get too tied up in the trouble checks - if your engine quits, once you've switched tanks and turned on carb heat if you have it, and any extra pumps, the 80/20 rule tells you it's likely not to start. But if you get the landing right, the rest is OK.
All this is a roundabout way of saying I think it's best to stay current with the basics, so current that you have a BOMBPROOF, PANICPROOF mnemomic that'll remind you what to do when it's necessary - which is to FLY the aircraft. Don't lose sight of the fact that when it gets real, your mind can play tricks on you, and it's the - endlessly rehearsed - basics that will keep you alive, much more than all the wiggling on anything moveable in the cockpit - with the caveat that the chances are good that if the engine has quit, you just ran a tank dry. That's my 2c, for what it's worth.
As a slight addendum, now I've practiced it so much, it's SWITCH TANKS, BOOST, CARB HEAT while simultaneously attending to those Llamas. Which was useful one day when I foolishly ran a tank dry on landing, in an aggressive side slip (double duh) - but it was gonna be a survivable glide anyway, cos the SWLFMRP thing kicked in straight away. It's gotta be, like, burned into your subconscious, I think, to ensure it's panic-proof.
Don't mean to subvert a technical discussion. I hope it's a useful thought.