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5000w is the minimum to do what you want. You're going to have a lot noise unless you go with something of quality like the Honda eu6500. The champion with get you buy but it will be loud.
Consider 2 Honda eu2000i units and a parrallel cable to connect them. It's a litlle more pricey but there are lots of advantages:1) Redundancy. Chance of both breaking down at once are small. You may not have 4k, but you're almost guarnateed to always have 2k.2) Fuel efficiency. If you are idling a lot, or running sub 2000 watt loads, you will use less gas than running one big unit.3) Each one only weighs 46lbs dry. Easy to move around and pack into small spaces. Only downside is the internal tanks are kind of small at 1.1 gal. I have an 8 gallon tank made for marine use plumbed to some aluminum replacement fuels caps and the pair will run a loooooong time.
Try solar1234.com. Steven Harris is brilliant. Listen to his podcast. He gives the info for free and discusses all the pros and cons of ALL generators. Plus he'll tell you how to use it properly.