You need: a good standard hammer;*
a set of Robertson, phillips, and square blade screwdrivers;
a Vice- Grip; a needle-nose and a broad-nose set of pliers;
a 3/4 metal tape measure @ 12 feet;
an electric, or cordless drill - a shop-vac for wet or dry is good to have;
an extension Light on a twelve foot cord is a must-have;
a set of spanners and nut-drivers various domestic sizes;
a combination nail-puller - crow-bar
a carpet knife; a roll of (wait for it) Duct-tape! ; an awl; paint-can-opener;
a soldering iron with solder and brass brush, flux;
a hand flashlight, some sturdy leather gloves and a small First-Aid kit to keep in tool kit.
A ladder is a good thing to have, but you can always borrow from the neighbour.
Lastly, you need a good toolbox, preferably a snap-on style, that you can snap a combination lock onto.
I hope that suits you. Anything less will leave you wanting at the time of a surprise repair
Home owner for thirty-five years. I have a heck of a lot more tools than I described, but you did imply BASIC!