Unless you want the lights on during the daylight, you'll need a 12V battery too, and a "solar regulator" gizmo to charge the battery from the panel when the sun shines, and supply your lights, phone chargers etc. whenever you need them.
The wiring is fairly simple ... but be very careful to avoid any possibility of short circuits setting the place on fire. There's a lot of energy in a fully-charged battery, enough to weld steel. Be sure to fuse each of the circuits with suitably-rated fuses. For example, if your LED lights need 50 watts, total, they will draw about 4 amps at 12 volts, so a fuse of 5 to 10 amps should be OK normally but blow if there's a problem. Your wiring should be more than sufficient for the fused rating ... otherwise the wiring becomes the fuse, and stringing a plastic-covered hotwire inside your walls is a bad move!
Bellwire is probably not suitable unless you only need very low power (~10 watts). It may only cope with an amp, maybe two or three if you're lucky. Heavy duty speaker wire has more current capacity, generally, but check the specs. Car & boat repair, electronics and electrical shops can supply whatever you need, all the way up to 100 amp+ "jumper cable" wire.
Oh and it's a bad idea to charge wet lead-acid car batteries indoors, without good ventilation, as they emit hydrogen and corrosive acid.
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