Shay ive been a semi pro guitar player since the 80s and I do teach Guitar mostly but bass occasionally, the Bass guitar has a very long scale so it can be a challange for a young person, go to a good guitar shop and ask for a short scale bass, dont take no for an answer, and if the wont sell you one walk out of the door, look to spend between 100 and 200 pounds I dont know whta that is in dollars, you will need a practice amplifier bear in mind you cant use a normal guitar amp the low frequencies will damage the speaker eventually.

find a reputable tutor and ask if you can speak to his/her other students to guage how appropriate the tutor will be for your youngster. I recoment a tutor that will teach both fingers and pick style, many guitar teachers simply teach playing with a pick, its better to know both. good luck