I think the OP's original statement of 3250 is good. look at the fuel burn between the 3250 and the 5k/6k. it needs just over HALF the burn rate.
I ran my home's fridge, CFLs, radio, ceiling fans, floor fans, and with discipline the microwave off a 2k inverter unit during the 5 day outage we had here. oh and the neighbor's fridge too. And I needed under 3 gallons per day, 24 hours on per day. 2kw inverter runs circular saw, shop vac, and other hand tools regularly.... i think a 1/3 hp sump pump is doable, however an inverter unit would probably have to be "eco-off" for the startup, especially if other big loads are present.
For that reason, a 2k is a bit small--- there is an above post that is so true--- you'll be frustrated that it isn't enough when you want to run more, unless you don't want to worry about storing much fuel. a 2k would work, if you don't mind managin the power carefully. A 3k would have given plenty, plus some headroom to run a space heater in the winter to keep a room tolerable.
When I had to back up the house, I made a quick 15A suicide cord during the outage, and hated it. it worked. As soon as I saved after that, I installed a transfer switch. I later read up on isolation switches, cheaper and easier and legal--- wish I'd done that. it's ok.
i then sold the 2k and bought a 3k. i stayed with inverter. why? 2k worked but yes there's wisdom in that it wasn't enough. if I was going to install an xfer switch, I might as well be able to make it wasy enough that we didn't have to shut down the house to run the microwave. Also, I stayed with an inverter because of fuel burn. you don't realize how hard it is to get gas.... until you can't.... and then you spend a lot of time a) monitoring what fuel you have b) worrying about burn rate c) driving waaay out to get it --- and all of the sudden you become a slave to the chore instead of just staying simple and working on cleanup, time with the family, fixing whatever damage you had, worrying about how to get to work...
do the math--- a 5k unit needs how much fuel to get you 5 days of safe food.....
random thoughts--- everyone has different expectations and tolerance. the fuel thing, hvac, hot water, will have different value depending on who you are. I want to sleep at night, which means the kids need night lights, fans to stay as comfortable as we can, and a heat source. that means duration runs for me.