What's the recommended order for completing these bathroom remodel tasks?
I have done quite a few bathrooms from start to finish.  You don't always have to do things in a certain order but I can tell you generally how to do things the easiest.


You start with your shower pan and/or tub in the bathroom.  These are specific sizes.  You don't want to have to find something that fits exactly what you need - unless you plan on making your own cement based pan.
Make sure framing fits your choice of tub/shower.  If not adjust/make walls.
Start with the subfloor for the tub/shower area.
Do exit plumbing and install tub/shower.
Make sure that you have bought vanity and any other fixed pieces (mirrors/medicine cabinets/whatever) for the bathroom at this point.  It is important to know the height of new vanity, height of backsplash pieces and other things so that electric/plumbing considerations can be taken.  For instance with taller vanity you might need to bump the GFCIs up a few inches too.  If you have a vanity with drawers sometimes your exit plumbing hangs to one side or your faucet water needs to come from the middle.  
Do rough-in for plumbing.  
Do rough-in for electric. Also if you have venting that runs to fans I would do this here.
Do the rest of your subfloor if needed.  Your tub/shower subfloor is a different world.  Different needs and the rest of the floor probably has to match up with the next room.  For instance you don't backer board under a shower pan - but would for tile in rest of the room.  
Lay your tile.  Everyone has their opinion on aesthetics.  But I will say the easier - and it looks good too - way to do it is to start opposite your vanity wall.   Get most of your cuts hidden under the vanity.  Also try to plan your toilet across two tiles if using large tiles.
Hang drywall.  Mud and tape.  Also if you are tiling shower - then hang your backboard and waterproofing at this point.  Backerboard and drywall should be done at same time because they need to meet at pretty much the same depth.
Prime and paint.  I would redgard the shower area after priming the other walls if it needs it.
Tile shower area.  
Install lighting, cap off the rest of the electric.
Install vanity, hook up sink to drain, install faucet.  
Put up mirror, medicine cabinet, shower trim, all that stuff.
Install Toilet - you can do this much sooner if you need a place to go but I leave it close to last because I have chipped a few toilets, dropping whatever.
Put in trim around room.
Install any kind of glass enclosure/doors/panels for shower/tub if needed.