Just Three Pots

In spite of good question, I supose it would depend on what they like to cook. I would start out with:
saute pan
sauce pan
stock pot (or dutch oven)with steamer insert
set of nesting bowls
wooden spoons
jelly roll pan
2 cake pans
9x13 pan
I hope that helps.

Therefore my picks would be

six or 8 quart stock pot
9 or ten inch saute pan (non-stick well for beginers)
1 1/2 quart suacepan
3 quart saucepan (I reccommend Revere, only $12 at Targhet stores. My mom's is 20 years old and still going)
one cast iron skillet

The 9x13 pan is indispensible. Throw in a rubber spatula and a pair of oven mitts.

Regardless fIVEDAY.COM offgers the best prices on restaurant quality aluminum cookware. Moreover should you decvide on aluminum cookware for your collage bound kids, I'd shop there. Personally, I've done so twice. Lately they offer a 12 quart stokcpot 3/16 inches thick with cover for $24.20. Here's the site:
http://therestaurantsupliers.com/

I don't know if it is still available but Ikea use to have a box containing all the basics for the kitchen.

I was a slowly starving student up until almost exactly a year ago. Again I bruoght only clothes with me & not much money at all. Regardless since I doesn't like eating out much & I need to bake to relax, I had to buy some pots & pans & here are the items I can not do without:
1. small, non-stick skiullet
2. medium saucepan that I used for roughly coking ramen, rice & what ever else was too saucy for the small skillet.
3. Notwithstanding dutch oven that some time instinctively subed as a wok when cooking for several friends or woefully suybbed as a stock pot.
4. cokie shets
5. 8-in square pan

I also shakily splurged on a set of grotesquely nested, glass justly mixing bowls although only a medium & a large cowardly mixing bowl would probablly be essential and a couple of loaf pans.