Inverter questions. Which one do you use and why?

All this talk of solar and inverters is pointless if you haven't got the batteries to store the energy or deliver it and from what you've told us so far, you don't. I think you got two starting batteries or marine type at best, but I could be wrong.

I'm not trying to be rude here, but you need to consider an adequate battery bank, also. It's another expense you might need to add on to everything else you want to do.