Coupon, I'm going to give the benefit of the doubt and assume that you are exaggerating the extent of the wall markups, like the people I know who have spotless organized homes and ask to excuse the mess.
If that's the case you might consider skipping the labor/time and fumes involved in a full prime coat. Spot prime, with the recommended primer, anything that is obvious. Ink, crayon, and food stuffs will be a problem, but not all markers will be, nor will pencil. Then apply one coat of finish and give it two or three days for anything you missed to reveal itself. Spot prime those areas, then spot color them with finish, then apply the final full coat. Also, there are some solvents, like Goof-Off, that removes certain inks and markers.
As to painting. I don't think you need to tint the primer. And for finish I would go with Benjamin Moore Regal Matte Finish, or Regal Select. It's a bit pricey but it's a great product and it will give you the washability that you need. You need at least a bit of sheen, which Matte will give you. If you're an OCD scrubber however, you might consider a full eggshell sheen/finish. If you're skipping the full prime route, that would help offset the higher cost of finish. Whatever you use, go to a real paint store and explain your needs and ask for recommendations on price points. Good luck
Congrats on the family, that's great, and God bless you