Cheap, they grow out of them so dang quick. If you need waterproof I’d get something of that nature. I just got my son a pair of Rockies I think. He liked them. I’d be surprised if we get another season out of them tho.
I'd go for something insulated and get him some gaiters. We've been through a lot of boots for the kids and I don't have one that worked best for all of them but probably the Under Armor were the most popular. With three of them I don't mind spending a little on gear, we get multiple uses. Depending on how far you might trek and how steep the country is you might also consider some of the insulated Muck boots with a good sole. These are great in the cold but not for really steep, long days.