I will not give you, or anyone else parenting advice. I am not one, so I have no experience in that field. Mine is electricity, and... trains (model sort, and live sort).
My comment about the flashlight was practical, if all you want is lighting.
However, if you are going to put a small TV or other electrionic up there, then of course you will want 110VAC.
If you can, purchase a 1,000 ft spool of 12/2 UF cable. It will cost you the same as or less than the three 250 ft rolls.
Some of the suggestions to install some yard lights, and maybe a couple other receptacles along the way is a good one. Why not get everything you can from this install.
Using the voltage drop calculator at:
http://www.csgnetwork.com/voltagedropcalc.html, you will have a 14.4V drop with a 5A load.
Note: Remember that when using this voltage drop calculator, enter the length of cable you will use from the house to the clubhouse. The program asks for 1/2 the length of the run, but remember that the total run is out and back, which for you woudl be 750 X 2 = 1500 ft. So you need to enter 750 for the calculation.
Whether that is acceptable depends on what the load is and what its specifications are. The type of power supplies that are used in computers will run on a very wide range of voltage, usually from 100V to 240V, but the old fashioned TV will probably not function properly on 100V.
If you think the drop will be too much, you can either run #10 (or larger) cable, or buy a transformer for the load end of the run. There are transformers, reguarded as "autotransformers" which can step up a low line of say 100V to 115 or 120V.
The transformer would have to be rated for the load of course, and be fused for that load, since it would most likely not be rated for the full breaker rating.
You could install the transformer for the devices that require 110-120V, and leave the lighting alone, since there would be no harm in having the bulbs a bit dim.
Another thought is to go with the new CCFL lamps instead of incandescent. They draw a fraction of the current the incandescents draw, but provide the same light. Example: a "60 Watt" CCFL only draws 14 Watts of electricity, while providing the same light as a 60 Watt incandescent bulb.
Note 1: Run this cable from a dedicated circuit breaker. If you are using #12 wire, I would use a 15Amp (not a 20Amp that is allowed for #12 wire), to prevent a load that would cause too much of a voltage drop.
Use weatherproof receptacles outside, and in the club house (since the roof could possibly leak). Use GFCI receptacles outdoors, and in the club house, or alternatively, install a GFCI receptacle in the circuit indoors before the cable exits the house, and wire it so that the run outdoors is protected by the GFCI.
Note 2: When I was a kid, I learned about voltage drop the hard way.
I ran about 75ft of #18 gage lamp cord along home-made utility poles from the house to the back yard, with a plug at the house end and a receptacle at the outside end.
There wasn't a real problem when I connected a spotlight (150W) or two to the cord, but when I tried to connect the electric coffeemaker one day during a family barbecue, and the coffee failed to brew, it didn't take me long to realize that the power was being dissipated as heat along the cord, leaving the coffee pot luke warm.
I replaced the 18 gage cord with 14 gage UF cable, and the problem was solved.
If I had to do it again today, I would use #12 cable instead of 14.
When you get to the point where you are ready to connect this cable to your service panel, do you plan to hire an electricion, or are you going to DIY?
Regardless of the fact that some people on this forum may throw in an "off" comment about the purpose of your installation, there are many more who are willing to help you with your electrical questions.
I am not a licensed electrician, but have done a lot of DIY, and understand how electricity works.
I am also studying the NEC (National Electrical Code) so that I can avoid the delays and extra work involved with failing an inspection because I didn't know about some minor detail that is specified by the
code.