Create an email address for the house and use it for everything house related. Contractors, mtg payments, instruction/owner's manuals for appliances, etc, all get sent here and it's very helpful. Also suggest doing a first look for manuals now. When you need to fix your water heater - even if you opt to pay a contractor - having read the manual first will put put you in a much better position to understand what needs to be done or what you are choosing to pay for.

Tool wise I'd include a couple pipe wrenches plus a 90° angle one for under sinks. The actual ones are probably less useful for plumbing inside the house but are just useful tools. A pickaxe is useful for small irrigation or electrical trenches. A pry bar for - you'll find a use. Someone else mentioned a hand truck which is really handy. Basic electrical tools, lineman plyers, wire strippers, an electrical tester. Some basic chemicals, acetone, alcohol, bleach, etc will come in handy for cleaning/prepping (don't store acids around tools/metal unless you put them in an airtight container as an acidic pH in the air causes rust). Other basic consumables are good too - a tube of caulk, electrical tape, couple boxes of screws and nails, plumbing tape, a small tube of epoxy, I tend to buy an extra of these kinds of things as I see them so that I have them when I need them. Once you have all this and other basic tools it's awesome to have a project and be able to do it without needing to go to the hardware store.

Not something you can just go buy but I keep an eye out for jars and drawers of junk at yardsales and thrift stores. Have bought a couple of little Grey boxes with the 30 tiny drawers full of odds and ends someone else collected - super handy. All kinds of oddball stuff, hinges, springs, rubber gaskets, cotter pins, that have saved me many trips to the store.

Outdoor bug lights - yellow bulbs that don't attract bugs. Not sure why I'd never heard of these but they make the patio more enjoyable. Not gonna keep bugs away but at least there isn't a swarm of them.

Good luck!