Begin with a U-store for the kids stuff, then get rid of all the baby stuff you are saving for the 'grandchildren'. When they show up you can shop at garage sales and pick up new stuff for pennies on the dollar.

Divide it into 3 catagories. Toss, Donate, Things I've used or worn within the past 2 years.
After that, I go thru the 'Things I used' pile again and eliminate even more stuff!

Box up the kids stuff and give it to them. They can carry it around or store it themselves.
I kept one box of my DS's stuff that I didn't want to disappear....certain papers he wrote in elementary school and a Winnie the Poo bear. All else is gone.

I am doing the same thing, but with my parents' house. I'll be remodeling it for myself. It is taking me forever. They designed/built/lived in the same house for 50 years, were teachers and volunteers, and my dad was an artist as well. They saved everything my sister and I ever made, etc. Years after retirement my mother still filed interesting things in "units" as if she would be called upon to teach a 3rd grade class about it.

My technique is probably bad - I went through everything looking simply for stuff to throw out. Then I went through everything looking for stuff to donate. Then I went through everything I could maybe have a garage sale with (we have few options here for donating) and put that all in one room. Then back again with the throwing out, since some time had passed and that gets easier. Now I am sorting the "keeper" stuff into boxes by category. I rented a storage unit a year ago for this. This summer, one day I went to the storage unit, hauled everything outside, and went through it again and cut it down by 2/3.

It is a long process, but worth it. As for my late parents' keepsakes - if it is a photo that they themselves are not in, I toss it. If it is a recipe that is handwritten I keep it- cut out of a magazine - toss.

Good luck. I am amazed at the stuff of mine my parents saved that they needn't have, although I appreciate the thought.