Bike for little brother

Recently, my mom asked me to get a bike from my 11yr old little brother. Was thinking whether to get him a BMX, small MTB or build a small MTB for him. My plan is actually to get a small frame and spec it with mainly deore parts, suspension is optional. 2nd hand small size mtb frame seems very hard to come by. Even when they are posted, their price is usually not my budget. Few weeks ago, i found a very good deal, scott yz1 with magura brakes, stem, handlebar and seatpost for $200. But due to my busy schedule, Im unable to meet up with the buyer. In the end the bike was sold.

Think I should increase my budget for the bike. Use it to setup a small street bike, at least it works out better in the long run.