Looks like a nice setup
Best bet would be a smaller size 12volt deep cycle battery and an isolator
Some can be seen here:
http://www.ebay.com/bhp/agm-battery-deep-cycle
The battery would be placed in engine bay and recharged via alternator thru an isolator
Isolator separates vehicles battery from smaller battery so running lights, radio, fan, ect.....won't drain starter motor battery so no worries about falling asleep with lights on, lol.
Deep Cycle batteries have thicker plates and are made to be drained down to 0 and then recharged, car batteries don't like that.
Just do a calculation on how many AMP Hours(AH) each device in the back might use
25watt light running on 12volts will use 2amps each hour
2amps x 5 hours = 10amp hours, so if you ran the light 5 hours you would use 10AH
If a battery was rated as 20AH then it would run that light for 10 hours without recharging
LED light use less amps so should be considered
If you only have the wattage of a device then divide watts by voltage to get amps
25watt/12volt = 2 amps
Cell phone charging is usually 1 amp steady but it drops to .1amps when phone is fully charged
12volt fans need to be looked at closely
Endless breeze fan draws about 3amps/hour
Schumacher 121 12V Oscillating Fan under 2amps/hour
And you can start with 20AH battery and then add another 20AH for 40AH, they can be used side by side.
The larger the wire you use from engine bay to bed the better, smaller wires heat up with AMPs and heat is a loss of AMPs, so the larger the wire the better.
And EVERYTHING gets a fuse
Fuse at the battery
Then fuse on and for each plug in or device in the bed