I had great success in using a water pistol to help train my kittens when I was home with them. All the family members had one at their disposal. The kittens would get a quick squirt if they went up on the counters, made motions to scratch the furniture or did some other undesirable behavior. Also used an old fashioned bike horn to honk at them when they were naughty. The sudden noise would scare them.
Setting the standard for what is not acceptable is so important to do at this early stage. Being consistent and vigilant when you are home will reinforce this wonderfully. When I could not be home, I had spread bubble wrap on the counters I wanted them to stay off of. Placed several sisal rope towers in rooms, hung them on door knobs and basically put other sisal rope scratchers everywhere. They had ample places they were encouraged to claw. I also frequently trimed their nails and handled their paws. We had tons of cat toys and played with the kittens with the toys readily. It was said that this would make the toys more desirable to the kittens to play with when they were on their own. I put one pressure gate above another on an open doorway that was a no-no. If you have double sided tape, you can put it down around the plants. Cats usually don't like a sticky surface. At one point I used those somewhat sticky nonskid pads where I didn't want them to be. I can't remember if it was paprika or some other spice I would shake on the dirt of the plants to deter them.
I would definitely pack or move your grandmother's antique lamp until you train them to stay off that table. I had people tell me that they put mouse traps under butcher paper on the counters to startle the cats and deter them off. I didn't do that one though. Cats are incredible explorers as you are finding out!