I can run 1 large or 2 small stove burners if the rest of the loads are down to bare minimum. In most cases, an electric dryer is out. Mine pulls more current than the electric water heater does, like the 6KW+ that Macgyver mentioned and it is not a monster dryer... Our small microwave works pretty well, but since it is around 1400Watts of load, on one leg of my 3KW total available, it tends to knock that leg down quite a bit and unbalance things. I bought a 3KW 240-120 step down transformer that I have wired to a special outlet in my kitchen. When we go onto genny power, the reefer and microwave get plugged into this outlet which is fed from the transformer. This spreads their loads across both legs of the generator equally and causes less disturbance to the power when in operation. Well pumps under 3/4HP should be OK. If I recall I have a 1/2HP pump and you can barely detect it's startup.
With 3KW, it is all about balance and planning. IF you don't have one, get a Killawatt. MCM electronics has them on sale I think for around $22 right now. Go around and start plugging in appliances and watch what they use average, and when starting up. I also find mine quite handy for remotely monitoring the generator. While setting in my living room watching TV, the only way I can really tell I am on generator power is the barely detectable thump thump thump. But by looking over at the Killawatt plugged into the wall I can quite accurately determine what the state of electrical load is as my set goes from 62HZ no load to 58HZ full load in a pretty linear fashion. When we cook dinner, the killiwatt gets moved in there, so if a load that pulls the gen down farther than 58HZ, we can just switch off a burner.
As an example, I can run every light in my house as they are just about all CFL's and present no real load. I also find that they show the lister flicker less than incandescents. Along with this, is a 400W pellet stove and 300-500 watts of entertainment center. This leaves 2KW for reefer, freezer and well pump to cycle as they see fit. I also have some installed forced air and small baseboard heaters in bathroom and bedrooms that can be run if everything else is caught up. My average load is not enough to keep my 6/1 properly loaded anyway. For dinner preperation, I shut down the garage breaker and take the well pump and freezer out of the equation so the burners can cycle as needed. Hot water will come from waste heat from the cooling system. I am also working on a wiring module that would allow the water heater elements to run at 120V to speed water heating for showers, but that will trip off line if a voltage drop is detected say when the well pump kicks in. this would help keep the average engine load up also. The washing machine runs real well, but other than having to use a cloths rack or line to dry, the 6/1 can provide all the comforts my family typically enjoys.
Good luck on your project.