Is he planning to also use the laptop as a laptop?
If not, there are small form factor PCs (especially if you’re willing to buy used business stuff) that don’t take up a lot of space that can be good options. Laptops have some features that are kind of nice on a server as well (the battery becomes a backup against power outages and you don’t need to remote access or plug stuff in to use it because it has a built in display and keyboard), but I don’t think they’re so nice that it’s usually worth buying a laptop just for that purpose. It’s more a reason that repurposing an old one makes sense. If you’re willing to pay the premium a new laptop adds, you can get some pretty low profile units.