What battery for my setup ?

Are you flying? Is weight (of battery) an issue? Will you be a (more or less) fixed vehicle installation (will you have vehicle alternator to supply some energy)? Size of solar panels (physical size), etc..

Various Li Ion batteries are certainly lightweight, have high energy density, and pretty close to the "ideal battery" (assuming you stay within their limits (do not over/under charge/over discharge--Picking the right chemistry will affect energy density vs excitement--Smoke and Fire if mishandled). Li Ion type are going to be best for (relatively) quick recharging (i.e., you can get a smaller battery and recharge quickly).

AGM are heavy, "spill proof", and a bit more stable vs Li Ions. (AGM can take quick charging, but you have to have the solar array and/or AC battery charger to supply the high current for quick charging).

Flooded Cell Lead Acid batteries are the cheapest solution.. Pretty rugged and forgiving. However, more or less, you can only recharge about 25% of capacity in an "average" solar day (10% rate of charge + 2-6 hours of "absorb" charging from ~80% to near ~100% state of charge).

In general, a small portable system is not going to be very useful for running a refrigerator (they take "a lot" of energy and run for many hours to cool back down--Generally more than a "small & portable" system can reasonably supply... Even evaporative coolers take a fair amount of energy.

Of course, anything can be done, but looking for more information to point you more accurately to something that will better for your needs.

And we need to know your energy needs (in Amp*Hours or Watt*Hours). For example a cell phone may take 10 Watts to recharge in 1.5 hours = 15 Watt*Hours (below assuming "per day" usage or 24 hour usage).

Cell phone 15 WH (1 day of average use)
Toothbrush and shaver--Ignore for now (generally those will go for days between charging)
80 Watt Laptop (that is a pretty large/high power one)... 80 Watts * 4 hours per day = 320 WH per day
120 Watt Laptop (lots of processing power, large/bright screen)... 120 WAtts * 4 hours per day = 480 WH per day
Refrigerator 120 Watt * 4 hours = 480 WH
Evaporative cooler (pure guess) 8 amps * 12 volts * 8 hours per night = 768 Watt*Hours per night
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1,631 WH per day

Assuming a flooded cell lead acid battery with 2 days of storage and 50% maximum discharge (for longer life)--Optimum for full time off grid use:

• 1,631 WH per day * 1/0.85 AC inverter eff * 1/12 volt battery bank * 2 days storage * 1/0.50 max discharge = 640 AH @ 12 volt battery bank

Or (roughly) 2x 6 volt @ 200 AH golf cart batteries in series (12 volts) * 3 parallel strings (600 AH) (6x Golf Cart size batteries--Not a small bank).

To charge such a battery bank, typically 5% to 10% rate of charge (10%+ better for full time off grid):

• 640 AH * 14.5 volts * 1/0.77 panel+controller deratings * 0.05rate of charge = 603 Watt array minimum 
• 640 AH * 14.5 volts * 1/0.77 panel+controller deratings * 0.10 rate of charge = 1,205 Watt array nominal 

And then there is sizing the array for energy usage and hours of sun per day:

• 1,631 WH per day * 1/0.52 end to end AC solar power system eff * 1/6.0 hours of sun per day = 523 Watt array minimum

Anyway, lots of questions (solar charge the battery bank during the day, and charge computers/etc. at night), or can you charge/run the appliances during the day (get away with a smaller battery bank).

Or bring ~2-4 liters of petrol per day and a Honda eu20i genset and forget the battery bank to run/recharge your equipment.

Lots of guesses, but it kind of gives you the thinking for sizing the system... Laptop wise, get a 30 or 8 watt laptop (save lots of power), forget the refrigerator and swamp cooler--And now you are down to 315 WH per day (or similar)--And a much smaller/more portable system.

-Bill