I recently setup a UPS using an inverter-charger. All UPSes that you buy at the store only have a short run time. 5-10 minutes at most with an actual load on it. I wanted a couple hours.
An inverter-charger is basically a UPS, except you can connect any amount of batteries you please and normally the batteries you'd buy for this will be much bigger, marine batteries. The little ones in an off the shelf UPS are maybe 7 amp hour while big ones you buy (for about the same price) are 100amp hour. You can even pay more and get higher end AGM batteries meant for solar systems and some of them can be 150 or even 200ah. Only downside is most inverter-chargers are 12vdc and not 24vdc so there's a bit more efficiency loss there. The more amps you draw from a single battery, the lower it's AH rating is. When a battery is 100AH, it means it is 100AH at a specific amperage. At a higher amperage it may be 80AH or even lower. I'm no expert on this so I wont really go too technical but you can find more online on this subject.
This is the UPS I setup:
I still need to setup voltage monitoring and a hydrogen sensor but otherwise it works. Yes, hydrogen sensor. If you start adding big batteries like this in your house it's something to keep in mind. they do produce hydrogen. Hydrogen dissipates pretty quick so it's usually not a concern but better safe than sorry.
My setup will run a 300w load for about 5 hours according to my testing. It will NOT run things like you mentioned though, stove or hot water heater. For that you're looking at a much bigger and expensive setup. 3000w+ capacity and tons of big batteries. You would not want to run this off a 12v system either, more like 48v. A stove is also split 120/240 so you'd need an inverter that can do that.
A UPS like my setup is good for loads up to around 1000w. Mine specifically is rated at 750w. I would not want to put more than 700w on it. So it will do a bunch of computers, lights, TV, that kind of stuff.
For anything big you'll want a generator. A UPS is good for stuff that cannot be momentarily turned off such as computers. Things like a stove or hot water heater can be turned off momentarily by the time you hook up the generator, not a huge deal. You can always look at a standby generator too if you get lot of outages that way everything turns off and a minute or even less later the generator kicks in. Also a good idea to test the generator once and a while, and have it run for an hour or two just to get the parts moving.