The cost difference is small (~$3) but well worth it. I would consider buying a stringing machine it will pay for itself quickly. I use an Alpha Revo 4000 ($650): excellent, crank handled table top stringer.
Again this is what we are using. My daughter is 12yo, 5ft tall and hits a strong, heavy ball with a semi/full western grip with an Aero Pro Drive babalot racquet.
Mains: Technifibre black code, 17G, 49 lbs (moves well across the cross strings to help with spin), $13/2 racquets strung
Crosses: X-phase one, 16G, 54 lbs, $16/2 racquets strung
Absolutely no problems with arm, good control and touch while still able to create strong spin. She plays 4 time a wk, 3hrs/day during the week and a tournament every other weekend. Will lasts about 3 weeks but I usually restring every 2 weeks.
Here is a good,brief article about how to choose strings for junior players and prevent injures from using polys.