Provided a charge controller is used to prevent overcharging, I would not worry about placing the battery indoors.
The amount of hydrogen emitted is very small and most unlikely to be a hazard, provided smoking, sparks and open flames are kept away from the battery.
Remember that until very recently, electric wheelchairs used vented lead acid batteries, these were normally charged and used indoors, also many garages are used as workshops without the vehicle battery being considred a risk.

Standard car batteries are not suited to regular deep discharge, golf cart batteries would indeed be far more suitable.

I would use 12 volts, not 24 since a greater range of lamps are available.
Remember that you may need to oversize the wires compared to a 120 volt circuit since voltage drop would otherwise be a problem.
I suggest a minimum of #12 wire on a 10 amp fuse, it would be prudent to install at least two circuits.
12 volt compact flourescent lamps and LED lamps have about the same efficiency, but the LEDS are generally available in smaller wattages.