First of all, welcome to the board!!
Many people think that declawing cats is merely like cutting our nails. It is not. Other people will also tell you that cats come through this surgery just fine. Some do, but others have infection, complications and great pain. Sometimes a deformed nail regrows, and must be surgically removed again. Some cats will take to biting, some will stop using the litterbox. Most probably don't, but this is a chance you take.
This is a mutilation that is done ONLY for human convenience, has NO benefit to the cat, and as such, I simply cannot condone it, and our rescue expressly forbids it for our adopted cats.
As for climbing the screen, this is something kittens do and he should outgrow it as it would be very uncomfortable for an adult cat to be hanging by his nails from a screen.
Learn to clip his nails. I clip my cats' nails regularly and keep them short.
Get a scratch post and some catnip. Make sure the scratchpost is VERY solid and doesn't move when your cat uses it. Rub some catnip on the post and dangle a toy in front of it to encourage him to stand and scratch.
Never play with your kitten with your hands, and don't allow your child to either. Always use a toy to play with cats, so they never think it's o.k. to grab and scratch hands.
Here is an article on declawing.