If I just straight into a giant project,  I feel like I'll either have to spend a ton of money to get something done professionally, or end up with a lot of costly trial and error.
			
		
	Perhaps this small project might help you out. I've tried to keep the costs way down, and still be somewhat useful with a a good deal of quality for their price range. The task at hand will be to just keep a 40-60w equivalent LED / CFL bulb burning for 10 hours to help get through the night. Use your favorite lamp fixture.
You might want to gather up these essentials:
1) Amprobe AM-510 multimeter
2) Renogy 50 watt 12v monocrystalline solar panel
3) Morningstar Sunsaver 12v / 6A solar charge controller
4) Samlex SAM-250-12 volt, 250 watt DC to AC inverter (careful, this is now 115v ac like from your socket!!)
5) UBG 12220 12v / 22ah agm battery or similar. Don't go with fly by night outfits that will sell you an old one...
6) Battery Tender 1.25A battery charger, either model 021-0218, or 022-0185g-dl-wh (the latter is the latest CEC high efficiency model)
The Battery Tender ac charger will help you get off on the right foot by ensuring that the battery you get will actually get a full charge from the outset. This is very important, and of course can be used when there is no sun.
The UBG12220 is a pretty common ups-style agm battery, but there are similar little agm's like CSB EVX12200, PowerSonic and so forth. Just beware of deals too good to be true. Try to go reputable.
Samlex is a quality inverter, and is what will drive your LED / CFL bulb for 10 hours. Try not to exceed 10 hours from one of these fully charged batteries. That will give you the longest life.
The Morningstar charge controller is of high quality in this price range, and you should remove the "jumper" for these agm batteries, even though the silkscreen says "flooded", because in THIS instance, this product's voltage with the jumper removed matches the requirements of an agm better.
The Renogy 50w solar panel is of relatively decent quality for the inexpensive end, and should recharge the battery IF you have 4-5 hours of good solar insolation. This means 4 hours centering around noon +/- 2 hours each side, and is NOT total sunrise to sunset hours. We don't know where you are, so if your hours are worse, especially with winter coming up, consider beefing up the panel to an 80W - 100W panel.
If it doesn't fully charge during the day, we'll pretend that the Battery Tender is a generator in disguise, and use that to finish!
Last but not least is the all-important multimeter mostly for measuring DC voltages. Don't get a shirt-pocket model. An auto-ranging meter like this Amprobe in this price range should suffice to get you started. THIS is where you will learn the most as you watch voltages during the charge / discharge process, do simple "rested" SOC battery terminal voltage readings to ballpark your state of charge, and the like.
It seems like a lot, but at least these are products that are quality enough not to make you question if anything is working in the first place. From here, you'll have the knowledge to make more informed purchasing decisions in the future based on your needs (the Kill-A-Watt meter is very useful for this), along with this forum's guidance.
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