In my cat owning experience: @Taciturnu Has the best answer as it involves little human involvement and works on most surfaces
Contact paper, double stick carpet tape or duct tape loops will do the BEST job of keeping cats off from objects you don’t want them on. If you put tape sticky side out on furniture corners & tops (couches/chairs/etc) your cat WILL NOT scratch on them.
As @syz said, a booby trap/scat mat will work. My only problem with this method is we have had “smart” cats figure out precisely where the stuff they don’t like is and then have found a new place to leap to. The sticky paper is SO undesirable they stay away.
If you do this and offer a good scratch toy, a good play toy, and one acceptable place for them to leap to you should have little problem with them exploring your counters, scratching up your furniture, or taking your stuff to play with.
For our cats contentment we offer:
one windowsill bed, several scratching disk toys with balls/mice in them (under a footed sofa), occasional catnip and treats, one scratching post(in an unused corner), a few purr pads on furniture we are okay with sharing and on floor space (under/behind furniture), and a few soft balls & mice (which usually need to be found by us——sometimes the cats even “ask” us to get them out from under furniture)...
We currently have four cats. One of them is a year old from the wild. She was quite an explorer and was tamed fairly quickly. We do use the “water bottle method” when she gets to riled.