Wow! thanks everyone for your responses. What a wealth of knowledge and experience..
I should have mentioned that I will be using a Conext SW 4048 Inverter & Midnite Solar Contoller. The thought is to use it with a Conext AGS.
From what I've been told, with home generators it's usually best to aim for a generator that is double the wattage of your system, so in my case that would mean an 8kw gen.
As mentioned by a couple folks here, by the time you'r at that size in portable generators, they are very loud and running at full throttle all the time.
I think I'll get something that can be coupled, and start with one, maybe this one:
https://www.championpowerequipment.com/product/100396-3400-watt-dual-fuel-inverter/ to see how well it can keep up, and buy a companion if needed. They run at just under 60 dba.
As John said, it would be nice to live in the house for a year or two and figure out what my needs really are before spending a big pile of cash on a generator.. This seems to allow for that.
Alternately I'd been looking at the honda 2200i companion option, but price wise it's way more.. I know they're great, I've used them on job sites, and the weight and quiet is amazing..
No auto start with either of these, but as I'll be ironing out kinks in the system, it might be good to physically go to the shed and check on batteries etc. at first.
I also found this one
https://westinghouseoutdoorpower.com/products/wgen7500df-generator-dual-fuel which seems like a nice compromise of all the aspects I'm looking for. Quiet for the size and style, reasonable price, portable, powerful enough... but I seems to be completely unavailable to buy at the moment...
Thanks again for all the info and suggestions. super helpful!