Basically, the 180 VA per outlet rule is waived for residential and you can have as many as you want. Space them every 3' (or every other stud while alternating sides) and within a foot or so of each corner as you never have enough outlets depending upon where the bed and furniture goes in a bedroom. Don't forget an outlet or two in a closet. Put a GFCI as the first one in the run and of course in the bathroom and the utility room and near a sink or washer, etc.
Rule of thumb is about 500 to 575 sq.ft. of floor space per lighting/outlet circuit. I would put lighting on at least 2 different lighting circuits which are different than the outlets incase a breaker goes in a room, you don't lose lights also. Your longest light run can be a 3 wire so you can put a connected system of 120 volt smoke detectors in each room throughout the basement as now required.(if one goes, they all go off)
No particular rule on boxes,except 18" for accessible outlets, otherwise rule of thumb is hammer height. I use 12" from floor to bottom of box. Some go to middle of box and I have seen some that go 12" to top of box with the idea that cords usually hang down to floor anyway. In basement with possible flooding, I would go 12" to bottom of box. Switch box rule of thumb is 44" to 48". I use 48" from floor to bottom of box. (it may depend upon your height and what is covenient to you. To be uniform, use the same box height as you have upstairs. Use the deepest boxes you can find as it never hurts to have extra room in the box. There may be places where you want a double or triple box(for duplex or triplex outlets)(also use pigtails on the terminals) or bigger if you know you will need it for a tv, vcr, satelite dish, radio, lamp, clock, phone power adapter, and computer/printer/monitor equipment that may be grouped together.
Rule of thumb for wire runs is about knee height, but I go 22" above floor which is then 6" above the box. This is about minimum as you need to staple the wire within 12" above the box (you also need to staple every 4.5' on long runs along joist. Drilling the hole 8" above the box may be better. Leave at least 8" of stripped sheathed electrical cable sticking into the box with a half inch of the sheathed electrical cable sheath exposed inside the box and the rest stripped off. If running through floor joists, drill your holes with the edge of hole a minimum of 1.25" from the bottom.
Use 12 guage nmc (the c is for wet locations)sheathed electrical cable wire with ground. It costs only a little more and you have so much more versatility for the future. Plus if someone novice puts a 20 amp breaker on 14 guage, you may have a fire. Many electricians don't use 14 anymore except when bidding in tract houses.
GFCI's as mentioned and in wet areas and unfinished areas. Use plenty of circuits with one for bathroom, another for high wattage heater, another for washer, 10 guage wire for dryer, another for whirlpool tub, etc. Some put a computer on its own circuit to avoid interference.
I understand about inspectors and agree. Take pictures of all wiring when done. He is supposed to inspect before you can cover the walls. Maybe you can keep him out of the house if you take him some pictures. It will also help later when looking for studs, etc.
Run cat5 8-wire phone line along with 2 runs of shielded RG-6 tv cable separated from the sheathed electrical cable by at least 6 inches in a parallel run. If not sure of phone and tv locations, cut a 3/4" or so notch in the front of the top plate (to be in front of any insulation) in each stud cavity so you can fish it down the wall later on after you drywall.
Good luck. Get yourself a good book such as Richter's 39th wiring simplified (99 NEC code) which sells for $5 or $6 at any home center. The 38th is OK. Search for some electrical sites here on the net.