That is quite a broad question. check your loads and see if it will work for you. I use a gas dryer with a push button start circuit and a dish washer with the element disconnected. my sump pump under load will not either. 3000 watts will not work for either. 5000 watt was giving me alarms till I connected bigger wire to the output board.
As Tom stated you need to consider what the home needs to operate. The size of the home is not as much a factor as what your planning on running in the home. I ran a 2400 pure sine wave for years till I converted to 24 volt. I don't have a dryer, my stove and furnace are propane as is the on demand hot water. I never had a issue with my water pump but I have a slow start pump which is designed for solar applications. I in a full size fridge and upright freezer, TV, lights, laptops, microwave in addition to the above. Things that produce heat( electric stove, toaster ovens, electric hot water) will kill a battery bank quickly. My place is about 2600 sq ft three bed rooms, three bath rooms. I don't consider it a small home but there are some that would consider it as one.
Thanks you guys for your replies, very helpful. My wife and I are working on going completely off grid. We have a small 16x40 prebuilt building and we are finishing the interior ourselves. Long story short is we currently use a 1500 watt inverter now to run lights, small fridge, and even our well pump but we cant run all at the same time. As the time gets closer for us to live full time at this house I'm a little overwhelmed as to how to 1) get a bid enough inverter to run our entire house and 2) get the power into the house without running tons of extension cords. With that being said we plan on heating with wood stove, use a propane stove, would like to get a bigger refrigerator and we don't use microwave. I do not have the hot water or air condition figured out yet but living in mid-Missouri would very much like to get some kind of air condition.
Definitely propane on demand hot water is the way to go as you only use propane when you turn on a hot water tap. You can get one that uses no power what so ever if vented up a chimney. The movement of water creates the spark to ignite the propane. Mine is direct vent so it uses a bit of power to run the venting fan. Get as big of inverter as you can afford. The top guys have a charger built in which you can use with a generator or grid power to charge your batteries if needed. In any case hard wire it into your fuse box and don't use any outlets which may be on the inverter There are wall mount aircons which can be powered with two grid tie panels these also will produce heat for the winter months Though I suspect not enough to heat a home but it would cut down on the amount of wood you'd need to heat a place. When I picked our fridge I looked for the most energy efficient one on the market without going to a DC model. After wards I noticed it had 6 25 watt lights inside I converted these to 1 watt LEDs so it is even more efficient (when the door is open)
Consider splitting the house over the 2 inverters. If you have a 1500 watt inverter that is able to do your well dedicate it you the well and maybe lights then use the 3000 for the other things.
So what is the difference between the 3000 w. pure sine wave inverter and just the 3000 w inverter, besides the price? Is the pure sine wave worth the extra money?
You can run just about anything but motors and certain electronics with a modified inverter. So if you are using it for house loads washer,dryer,refrigerator,dishwasher,sump pump,furnace blower,garbage disposer, spend the money for a good pure sine wave inverter. Low frequency is better. But my high frequency works fine after a few easy mods. Check my Post your photos. I have to watch how many loads I run at one time. So far the 5000 watt is able to keep up. The 3000 watt would not run my dishwasher,dryer,sump pump,furnace blower.
A Pure sine wave inverter puts out the same clean power your utility does. Although almost any thing will run on a modified or Square wave inverter, most if not all things life expectancy is reduced as they are slowly damaged. It isn't just the heavy load items that will get damaged small electronics will fail faster if they work at all. I've ran both types and the pure sine wave inverter is definitely worth the extra price.