If you ask the family, expect the answer to be "Yes, and the MargaritaMaster-9000 as well."
When it comes to heat of any kind (room, food, fish, etc) the general response is "Anything but Solar" because of the massive system required. To give you a little perspective, a bog standard 100ah LFP battery will run a bog standard electric heater for about 45 minutes before it's dead.
If you want to poll the family for their needs, rather than ask them what they want to run, list out different things (fridge, aircon, internet, Margarita-Master-9000, etc) and have everyone rank them from most to least important. Then figure out how much system you want.
Once you have your power audit (how much inverter + how much battery + how much panel) then you can figure out what kind of battery you'll need and go from there.
As for which cells to get, it's going to depend on one other factor and that is portability. Can you build a honkin huge battery on a shelf in the garage or are you going to need to pick it up and move it around? Trying to move a 16s EVE280k battery is MUCH different than a 4s 100ah battery. Physics and your back are gonna "Have Words" if you don't take that into consideration.
The current Bang-For-The-Buck cells seem to be the EVE-280k's for high density. Considering you can buy a 100ah LFP for about $170 now, but the same cells alone are about $220, building a battery isn't really as cost effective as it once was. The advantage to building is the higher capacity cells are a better value and it's a LOT more fun.