I have a 5000 Watt for the cabin. I cannot remember the make but it powers my stuff just fine. I run it in conjunction with 4 batteries and 4000 Watts of solar. It was right at 400$.
Yes, if your not depending on it.
A pure sine wave that size will not be cheap,... if you can get away with a modified/square wave they are much cheaper, but even at that the quality units (2-4kw)are still not 200 bucks.
I bought my first one at a town pump gas station, it was 1000 Watts and cost 60$. I ran it daily for almost 2 months before it crapped out on me. I know plenty of folks powering their home with a HF generator.