I've been using a setup just as you describe quite reliably for the last 3 years. It's a DC inverter rated at 1500W (peak 2100W). You can find one for under $200 if you shop around. Mine comes with 3 A/C outlets on it and I just use one to backfeed my service panel through an unused 220 dryer outlet. I just select the circuits that I deem "necessary" and have no problem during power outages.
On the car side, you'll need beefy cables that connect from the car battery to the inverter. #4 or larger for this size inverter. They can be a pain to work with, but you will be maxing out the battery under full load and need them. My alternator is 130A, so I have no problem keeping up with full load. I suspect you can get away easily with a 90A one - but not much smaller.
On the house side, I take the 110 from the inverter in to a 220V plug that has the 110 hot crossing both 220 hots. The neutral and ground remain normal. Throw ALL breakers in the main panel and connect the plugs. Now, turn on 1 breaker at a time for where you want service and you should be fine.
My main concerns are heat and the fridge when we lose power. My inverter keeps up with these things plus a few lights and small TV just fine.
Make sure your car is running when you try to use anything with a small start load. If not, the inverter will draw too much juice and fail to start the appliance due to lack of input power from the car.