We are not connected to the electric grid, yet have a full sized "normal" refrigerator, a freezer, three computers, three TVs, electric washing machine, power tools, a bit plotter (a printer for blueprints), lights all over the place, kitchen appliances like Kitchen Aid stand mixers, etc. We do not, however, leave the lights on or run things that make heat like hair dryers and toasters. The air pop popcorn popper pulls 1,475 watts and our inverter (the magic box which changes battery power to regular household current) can put out 1,500 watts. So I have to turn everything else off while I'm making popcorn.
There is an electric pole for our neighbor's house right at the end of our short driveway so we could be connected to the grid without any additional power poles. In our case, though, we don't have a building permit so the electric company didn't want to connect to our house. After we installed the photoelectric system (four solar panels, the inverter, a charge controller, fused switch and eight deep cycle batteries for $6,800) we then found out we could have connected to the electrical grid because our house doesn't need a building permit. It was built prior to 1915 and has documentation prior to 1930. However, we are now invested in Hawaiian Electric and they pay us dividends and we don't have to pay them.
Since then, we have gotten four more big solar panels and now we run the backup generator much less. My DH is good with engines, so he found one which wasn't working well at a yard sale and he fixed it up. Eventually, we will get a small wind generator, too, but we are in a fairly windy area.
Let's see. Specific off grid advice? Curly bulbs are your friend. Incandescent light bulbs are evil. When you wire up your house - it is just like a "regular" house except where the electric meter would be is the solar system. Anyway, when you wire it up, make some wall outlets have an on/off switch on the wall above them. Plug in anything with an "instant on, timer, or standby mode" into those outlets and turn them off when you aren't using them. Otherwise, be very aware of how much power is being used. I like to do laundry on sunny days.