Perhaps a 1,500 watt one (about $700.00+). I like the combo inverter/charger models. The 1,000 watt Heart has a 50 amp charger. You could go with a Xantrex 1.000 watt inverter/charger for about $400.00+.

I wouldn't worry much about the sine wave. For the most part the only thing that will give you trouble is refrigeration. We've been using a Heart 2,500 watt inverter/charger for 10 years and haven't found anything that doesn't work.

As you said, your biggest concern is your battery bank, 1 group 31 is a small battery bank for cruising. As Larry brought up, you don't have many amp hours. You might think of doubling your bank. ,,,,, Yeah,,, put in a 1,500 watt Heart inverter/charger (don't worry about the sine wave) and double your house bank. You should be in good shape.

Don't really listen to me. It's only a quick thought before my second cup of coffee.