Not sure if I'm the right person to give advice given the state of our bedroom...but I'll blame the Boy for that. I'm not gonna be the one to put away his stuff. ;)
My process tends to go from the most noticeable/in the way to the deep-cleaning stuff that you have to look for to know about (and no one will).
First, declutter. For us, stuff builds up on tables (coffee/dining/desk): mail, papers, books, electronics/cables, scattered coasters, etc. In the kitchen, this is putting away clean/dry dishes and washing the next batch. In the bathroom, anything that got left out on the vanity.
Next, clean surfaces, top to bottom. Damp rag for dust/crumbs, vacuum on floor. Vacuum spiderwebs in corners or ceiling. In kitchen, wipe down counters and stove, with cleaner if there are spots and scrub kitchen sink (it's a kind that gets extra grody really fast...enameled, I think). In bathroom, Windex mirrors, wipe vanity (maybe with cleaner), wipe handle and rim of toilet with cleaner, inside with bleachy cleaner and brush.
Finally, deepest level/special project: mop floors, clean all around toilet and bathroom floor, wipe baseboards and/or cabinets, scrub kitchen counters with Comet and brush (they are tile), scrub tub, clean out pantry or fridge or closet, clean oven, take off burners and wash/scrub drip pans...those sorts of things.
I usually do "first-next" kitchen cleaning daily, we pick up and vacuum every few days-week, go through the "next" list weekly, and handle deep/special projects monthly or less, as needed.
My arsenal is probably unmustachian but bf and I both hate the smells of vinegar, straight bleach, and ammonia. So I keep: dish soap, Windex, Fantastic, Meyer's Basil All-Purpose Cleaner, Pledge Squirt-n-mop (doesn't leave a sticky residue), Comet, and Chlorox or Lysol (I forget) toilet gel. Oh, and we have tiny things of Goo-gone and Wine-out ($1 ea from Target). 8 months since we moved in and stocked up on all this, we've only had to replenish the floor cleaner, everything else is half-full, and each of those is <$5. And of course, we have the household staples not exclusive to cleaning: baking soda, bar soap, rubbing alcohol, nail polish remover. I use rags for a lot of things (old sheets and towels, cheap washcloths if I run out), but paper towels for mirrors and toilets. I also wash the rags separate from clothes--threw in our bathroom rug with the batch this weekend. Although frequently, I just keep downcycling them (counters to floors to bike to trash).
Handy tips (I think...):
-In my experience with vacuuming, frequency is more important than thoroughness. And if you have a big, bulky cleaner, you'll be disincentivized to take it out. At our new apt we got a
http://www.amazon.com/Electrolux-Ergorapido-Handheld-Cordless-EL1022A/dp/B005DSK72A and it sits in its charging cradle in the living room and it takes literally a minute to grab when you notice a mess. It's also super maneuverable. Wish I knew this when I lived with a dog (roommate's). *side note* this particular model sucks at carpets, but you can probably find something similar that doesn't, if you think this strategy is right for you.
-A waterpik water flosser, if you have one, makes a great scrubbing tool, esp for tight crevices. I get it out to get the scum out of the rim of my sink, stuck food from the corners of my Ninja chopper, tough mold off the tub tiles. Since the device stays 6" from the mess, I have no qualms sticking it back in my mouth, either. It's like a mini power-washer. Just be careful of anything that can break/flake off (e.g. grout).
http://www.amazon.com/Waterpik-Waterflosser-Cordless-Rechargeable-WP-360W-I want to second the idea that you shouldn't try to do everything in one sitting, but focus on 1-2 rooms. I start cheating when I get tired. Better to clean it right the first time...the next day.
-I second the idea of music. :)