This topic is so difficult for me because I am passionate about it. This post is for the parents who want their kids to be better... by having multiple pitches.
I run into a lot of intermediate, even beginner students who say they have 3 plus pitches. There are a lot of professional and international pitchers out there who can get away with throwing two pitches for an entire game. If they can do it... your 8 year old daughter can go through her game without having to throw a change-up or a "rise" every time she has two strikes on a batter.
I believe in mastering one pitch before you move onto the next. One pitch takes months to master, and trying to master two at the same time takes twice as long. So not only is perfecting your craft hard on your mind but it is hard on your body. Hitting your spots is more important and once their body has developed and their muscles are stronger... and they have the stamina to perform vigorous wrist movements and a finger snap, then you can push for movement pitches.
Basic guideline? It's hard to determine by age, because everyone develops differently... so this is very general.
Ages 10 & Under : 2 pitches (Fast & Change)
Ages 10 - 12: 2 pitches (Fast (low fb / high fb) & Change)
Ages 12 - 14: 3 pitches (Fast (drop / rise), Change, Curve)
Ages 14 - 16: Master the Change & a secondary KO pitch (drop, rise, curve)
Ages 16 - 18: Should have 3-4 pitches at this point and 2 of them should be your go-to's.
*** Notice, I avoided the Screw Ball. In my opinion it is the worst pitch to learn until you are in the 16-18 bracket. It is a really hard pitch on your body and there are not a lot of coaches out there who know how to teach it properly. That is not their fault, everyone has their way that works for them, but a lot of the time it is not safe. Do your research, and be cautious.