Solar should NOT go directly to the batteries. EVER. You need a charge controller. The controller stops bleed back to the panels, and stops your batteries from OVERCHARGING.
Panels connected straight to batteries will overcharge and you will destroy the batteries.
When you get an inverter.. make sure it is a PURE SINE inverter. These are NOT available at WalMart. Camping stores, Amazon, etc. will have them. As a general rule if the inverter does not say 'Pure Sine' it is not.
A microwave will run for **** on a standard inverter (modified sine wave). Also, sensitive electronics will be destroyed. (New Mac's will generally not run at all on a modified wave inverter.)
Thicker wire is better (8ga or larger) and never place an inverter in the same area as a battery bank unless the bank is sealed and vented.