Oh boy, are you in for a treat. Well, if they are untrained kittens that no nothing, you will soon adopt the "stiff arm" where you sort of gently push them away from jumping right into your plate, or another good move is holding your plate above your head in between bites (don't have a clever name for that move). Kittens are bad, they are like little kids, they know nothing and have to be taught. Yes, by all means start NO, and make sure it is consistently NO, with a loud clap, stick to the one word, because if you just ramble at them and yell (like my mother in law) they will just look at you confused. A water bottle is something many of us have used during the training phase. A squirt of water is not liked well, and usually works pretty well, and after a few squirts, you just have to shake it at them to keep them at bay. I don't mind my cats so much on the table, because we rarely eat there, we too use the couch more often now since one kid is in college and one is never home, but I can't STAND them on the kitchen counter. So I use the water bottle and NO and Stephano, my youngest kitty, still will get up there when I'm not looking and I have to chase him down. Cats are not like dogs. They are pretty much going to do it anyway even if they know they are not supposed to. I have used the NO approach to scratching furniture too, and none of my cats scratch furniture, other when they are doing zoomies around the living room chasing each other in play, and you will hear the claws on the couch as they are running past, but they don't hurt it and they are not intentionally scratching it. I owuld highly recommend you getting a scratching post or better yet, a cat tree. It will save your sanity. It will give them plenty of exercise to run up and down, they will want to scratch that nice sisal post rather than your couch, because it is more desirable. I am also a big one for keeping a kitten confined to a room at night, I have always used a bedroom, that has a cat tree, a window, litter box and water. Give them a big meal before bedtime, that is a HUGE help, and establish bedtime routine. Then they learn, bedtime is for sleeping, because their natural instinct is to want to play during that time, but they can be taught that it's sleepy time. I also do not believe in letting kittens have the free run of the house until they have learned that they can't scratch the furniture, and they know exactly where they are supposed to pee. Once they know all of those things, then it's safe to let them out for longer periods of time, but if you do it while they are a kitten, they just tend to get into trouble, in my experience. You will want to keep the new cat or kitten confined to one room at first anyway, because it is less overwhelming for them at first to become used to a small room before the entire house. Once they get used to that room, then that will be their "safe" room, and they will run back to it when they are scared, and they will probably keep that room as the room that they go to when they are scared.
This is how I've done it with my cats. My cats are all well behaved, for the most part, after all, they are cats, and cats are little jerks that do what they want to do

and we love them anyway. But the NO word does work, it takes about 1000 times of doing something before they really start to listen to you. Good luck with your new kitty. Are you getting a full grown cat or a kitten? They are two totally different creatures, LOL!