First time home buyer, what tools are most commonly used around the house

Bottle opener

Husbands.

I got that question a lot when I was teaching night school for "Quick Fix Home Repair". I always told students this;
A comfortable hammer - smooth face , about 16 oz.
A multi-bit screwdriver ("PicQuic" is a brand name)
A metric/imperial tapemeasure - 12 foot is good
Some kind of wrench, like an 8" adjustable, or "waterpump pliers" / "spanner" / "slip joint pliers" e.t.c.
A utility knife WITH extra blades
(Band - Aids) becasue of the last one

If power tools are in the budget, I suggets (in order of necessity);
Cordless screw driver or gun (with bits)12v is all that is needed - DONT buy the 18 V, it's a waste of beer money.
Jig saw or circular saw. Jig is more versatile, but circular is for larger, bigger cuts.

Any other power tools can be rented for the occasional use.
Here's a tip;
If you rent it more than twice, buy one!

A hammer to hang pictures on the walls, a few screwdrivers and, if you have a garden, a few gardening tools - lawnmower, spade, etc.

Duct tape, Gorilla glue, mop, broom, tool set, fire extinguisher. garden hose, lawnmower, list of emergency phone numbers, burglar alarm, photos of all your assets inside the home, plunger and the list goes on.

These are the basics. there may be more.