Does he like eggs? So many cheap, quick and easy fixes.
Pasta, rice, potatoes, hot sandwiches, wraps
Alton Brown basics come to mind.
Hamburgers or sloppy joes
Pancakes, french toast
I lived in a trailer during college, mini kitchen in the front, elec stove top only for cooking until a small grill was permitted during the summer months. I lived on eggs, canned tuna, canned chicken, green salads, Kraft mac n cheese and pie…and the kindness of my landlord.
I gave all my nieces and nephews How To Cook Everything, but I kind of regret it. I think it’s too complicated for beginners. But Bittman also has How To Cook Everything, The Basics, which would have been a better choice.
I’ve outgrown actual cookbooks myself. I agree with others that the younger generation is probably better off watching YouTube or videos so they can actually see how something is made. I know you said counter space is limited. There’s always a plug in electric covered skillet. You can cook just about anything in that.
I got both The Joy of Cooking and the New Better Homes and Garden cookbooks when I moved out. As much as I love Joy, I think the latter is more accessible for a beginner.
Is he likely to read a cookbook or is he an internet guy (and from there, Web or app)?
My grandmother gifted me a slow cooker. There are ones that have inserts that let you brown foods in them now. That might be the way to go for a limited kitchen. I think ATK has a slow cooker book. Another thought would be a rice cooker. You can steam foods on top of the rice.
Due to a series of life circumstances, I’ve cooked several things from the website Pinch Of Yum this year. She does a series she calls SOS that might work for your situation!