Have you tried Williamson Music in Plano off Plano Pkwy and 75? They do a lot of rentals for band and orchestra involving beginners.
My daughter (now a 7th grader) started with violin and we rented a violin until she actually showed some talent and advanced into a higher grouping within the school.
We just recently purchased a violin (not cheap, looking at $3000+) but she intends to take it through senior high school and possibly more. We did not make our purchase through Williamson ( we did rent through them) but they do have a program that applies a portion of your rental costs toward credit for a purchase if you purchase from them.
The band/orchestra director at your school should be able to give you info on where they recommend you to rent an instrument. Most all 6th graders rent and take private lessons to see if they really do want to stick with it. After a year or 2, you then decide if your child is going to stick with it or not.
My daughter was given a choice as to what she wanted to do band? Orchestra? or Choir? THEN....the instrument choice. When she chose violin, we were given options as to where to go to rent or purchase. I live in Allen but I am in the Plano ISD system.
Good luck to you and your middle schooler. Things change so fast.