I’m also having some winter lighting issues... being winter it gets light out where I live about 8 am, full dark sets in by 5 pm. My girls are currently in a garage with lots of windows, but it still doesn’t really brighten up enough in there until after 10 am, and it starts getting dark inside well before it is dark outside. I’ve got flourescent lighting in there for them though... assuming other people don’t turn them off trying to be more energy conscious!
If you’re going to be on solar I would recommend checking out RV suppliers, and online. I don’t know if light spectrum is particularly important to chickens, if you’re just looking for supplemental light, LED is good for solar as it’s less draw on your batteries. You can get kits online with panels and a charge controller (protects your batteries from overcharging) at reasonable prices. You may need to buy some MC4 Y connectors as well, some kits don’t include them. I’d think 200 watts and two deep cycle 6 volt golf cart batteries would be fine for a small light system (you get almost double amp hours, useable energy, from 2 6 volts wired in series than 1 12 volt).
You will want to position the panels in full sun facing south-ish and approximately at the same degree angle as your latitude, though I think that’s somewhat less important... Point the panels at the sun, keep your wire runs as short as you can, and keep your battery box separate from the animals. Lead acid batteries off gas. There is lots of info online about how to set up small off grid solar systems.
I’m guessing $600-$900 USD for a decent 200 watt system and batteries, but that depends on where you’re living.