When I got my first apartment, my mother gave me a bunch of half full spice jars with handwritten labels. She had saved up her empty jars and gave me half of whatever she had. I thought it was a weird gift until I used up the first one and discovered how much it was going to cost to refill. That way I had some of everything and the cost to refill was spread out.
I also went through her recipes before I left for my favorites. She gave me a Betty Crocker cookbook (very fullproof) and a neighbor gave me a Joy of Cooking (what would now be an old edition, harder to use, but more recipes than Betty).
As for pots and pans, at least one each. A mixing bowl. Wooden spoons and a spatula. A good paring knife, large knife, vegetable peeler. A plastic pitcher. Some storage boxes for the fridge. Now I would add two or more reusable shopping totes.
I used a wine bottle as a rolling pin for a while.
You can easily stock up cheap by hitting an estate sale.