Well, anything signed or written in, I would certainly keep. It may not seem that important to you, but your kids may really appreciate them when they are older and who knows - if they are still in decent condition, they may keep them for their own kids. My mother passed away unexpectedly last year and I would love to have at least one book from her to my daughter with a handwritten message in it.
Then decide which ones are really worth keeping and which ones you think are better off donating. But it almost sounds like you need a better system for keeping and organizing what you have already. Time to invest in more shelves! Or maybe store a bunch of them and then "rotate" the books, like toys. Or try selling them on-line.
At our old house, we lived in the downstairs apt and rented out the upstairs. Each apartment had their own huge recycling bin out by the curb for pick-up every week. Our upstairs tenant had 2 little girls - around 6 and 2. One day I found a ton of perfectly good children's books tossed into their recycling bin outside. They were all the older daughter's books and I couldn't believe they wouldn't want to still keep them for the younger one. I don't know if the mom decided she needed more room, or thought they would somehow be donated rather than recycled. But instead I spent a good hour hauling all the books out of there - there had to be over 200 books, I lost count. Some I ended up keeping myself for my daughter and the rest got donated to the local Goodwill store.
I understand the "overwhelmed" feeling, but I would rather be overwhelmed with books than anything else.