I finished my basement - took ages to rip out the old walls and crap, redo the wiring, plumbing, some structure, lots of framing, chipping and redoing some of the slab, new staircase etc. Did it all (top notch I might add) for well under $18K but that assumes I was paid $0.078/hr and lost MANY weekends and evenings over 3/4 of a year. In hindsight I would have appreciated the work being done faster (dedicated workers during the days) but much of the work HAD to be design-as-you-go...opening something up reveals more work that could not have been known.
Having said all that, we have an awesome basment with a rec-room, bedroom separate (large) storage area and a consolodated and usefull utility/appliance work area...not to mention upgrades that benefit the whole house (more effecient overall), and we use it ALL THE TIME.
Our kids are 22 and 9 months and we finished a month before the youngest arrived. Priceless and super practical. Main floor living space is not a toy store/mess.
Added value? Simple look at the homes in your area, price range that are comparable size etc and see which have finished basements and what they are going for over ones without. I would think 10-15K if done well and is practical.
The rooms that I recall buyers wanting most were #1 Rec-room, #2 bedroom, #3 bathroom, #4 second bedroom/storage room #5 Whatever was not in #4, #6 workbench/'sewing room' space
...laundry, H20 tank, furnace, elec panel, etc are assumed to be there but preferred to be in the same area. i.e. water line not coming in a bedroom, sewer access not in rec-room, elec panel not in bathroom...
About the Nanny...cannot comment. Daycare is the way to go $-wise for us.