First step is to figure your total load for your piece. Get the specs for the lights, multiply x number of lights.
That should give you total watts. Divide watts/voltage (12VDC? 120VAC?) to get total amps.
Then figure how many hours the piece will be lit (10 hours/nights?) - this gives you total amp hours (aH). If you are running 120VAC, factor in ~15% efficiency loss for the invertor. (This is one reason a 12VDC system works well)
Your battery array should provide at least 10-20 times the aH of your piece. So if your total is say, 5aH, use a 100aH battery.
General rule of thumb = the closer you pull from a battery rating, the faster its discharge rate. So, a 10aH battery will not power a 5aH load for (2) hours. Lead acid batteries work best at a 10 - 20x discharge rate. Then factor in how batteries behave on the playa - this will also limit things a bit. Also, don't discharge batteries too low (10VDC) or you can kill it.
Example: I did a 12VDC solar-powered piece that used ~5aH. First time out, I used a 55aH deep cycle. That powered things well for ~6 hours, but at 10 hours the battery was about done. Second time out I used (4) 6VDC in series/parallel for about 200aH w/ (3) 100w panels - no problems at all and probably overkill.
For charging, figure a solar array that will supply the total aH during the charge phase. This charge phase can be all day if the panels are positioned well and you dust them off. An 85watt panel will source about 5amps @ 12VDC and would take 8 hours to recharge 40 amps.
When designing a system try to get everything matched and balanced: You want the charging system matched to the battery system. IOW, don't put 20amps into a 55aH battery. Also, get a charge controller rated 1.5 times what you think you'll need.
Regarding the 45watt HF deal: I have used them, not impressed. These were (3) 15 watt panels. As I recall each 15w panel was nearly as big as a Kyocera 85w panel.
In the past I have used these guys: http://www.affordable-solar.com/
FWIW, my current setup is (2) 85w, 15amp Morningstar charge controller, (2) 55aH Optima blue top, 300w SureSine inverter (no fan). I like not having to refuel a generator in the middle of the night, or anytime else for that matter.
Oh, this discussion is for deep-cycle lead acid batteries, not Lithium varieties.
So to recap:
total ampHours = total watts/voltage
charge batteries @ 1/10th rating
discharge batteries @ 1/10 - 1/20th rating
factor in efficiency loss for all components (10-15%)
Oh, good luck with your piece!