Take him shopping and if he doesn’t care enough to shop do it how you like it.

What's he going to do in the basement? Lots of friends hanging out = lots of comfy places to sit. Board or card games = table, chairs and storage. Will you allow food? If so, consider a small fridge and microwave. Movies and video games = a tv. Hobbies = work table and good task lighting.

Is he a packrat, minimalist, or somewhere in between?

Keep the walls a nice light color since basements don't get a lot of natural light. Does he have a favorite color? Don't assume it's blue just cause he's a boy! If he's not interested in shopping, go to the paint store and choose some colors that are acceptable to YOU, and give him a choice of only those. I think you can't go too wrong with white in a basement, and bring in color with accessories.