Generally speaking, wider in the nose is better for paddling and wave catching, narrower nose is easier to keep out of the water in steeper or more dangerous drops. Wider in the tail gives you more push from the wave and thus more speed, especially on a shortboard where your back foot is way back a lot of the time.
Width overall gives you stability. For numbers, 22" is wide, 21 is medium narrow, 20 is really narrow. And 19, well, if you can surf a board that is that narrow you don't need surfboard advice because you're already ripping and know your own preferences.
Length gives you glide. Suit your own preferences here, but unless you're really really really not getting that rotation on your turns as fast as your body pushes, more length and glide is helpful to many intermediates.
Lower rocker in the nose gives you quicker paddling, lower rocker in the tail gives you trim speed when on the wave. For someone in the vast realm of intermediate, that generally means you want low rocker throughout.
You're quite light so you can go lower on thickness, and may want to to get responsiveness and that feeling of being able to dig into the water in a turn. Talk to your local shop or shaper on this to get the numbers right though.
To summarize, wider and a little longer with lower rocker is the easiest short board to ride. You may wish to consider a board that is short but not a "short board." These go by various names like hybrid, stubby, or the smaller, thinner end of egg or midlength, but the thing relevant to your question is that they're wider and lower rocker but still short. A "high performance short board" is going to be narrower and more rocker than a "daily driver" short board is narrower than one of these hybrid/fun/stubby/whatever short models. Stephanie Gilmore talks about her enjoyment of this type of board here:
As far as specific models, ask your local shop! There's a huge variation in what boards work well in local waves. If your area is longboard centric, you'll need a lot more board -- length and volume -- to get waves. If you're surfing an all-shortboard break with a nice push to the wave, you can maybe get away with less. Also consider asking other teenagers of similar abilities in your area. (Don't trust the super rippers, they will tell you to get too much rocker and too small a board.) Also, if you buy used, you can usually sell for similar amounts if you get a good deal to begin with, even after a full season if you don't get a bunch of dings.
Good luck!