For the most part, it's right, but I'll try to iron out a few other details for you.
Puppetry was created by Monzaemon Chikamatsu, who originally created the art for entertainment purposes. It was later enriched as a long range fighting style.
Puppets are generally made out of whatever you can think of, metal, wood, etc and are used as weapons in fighting.
I want to more go over the weaknesses you've mentioned. While a standard puppeteer is limited in a short-range environment, a lot of people will keep a defensive puppet by their side to intercept an incoming opponent if they do decide to enter short range. Another factor is that they have to actually get into short range, which isn't the easiest thing in the world to do when they've got puppets in their face. So really it's a situational weakness, most puppeteers have something in order to prevent the weakness from happening: Kankuro keeps Salamander close by to use it's shield, Sasori has a number of mechanisms to stop people from coming close and so on.
Another weakness is infiltrating the puppets themselves and rendering them unusable. Some abilities can take the joints and rust them out, or at least jam them in place so the structure of the puppet can't move. Abilities such as Sand can achieve this quite well. Aburame is another notable weakness to the puppets since their bugs eat chakra and the puppets are fueled by it, making them strong against it.
So this next part of training is that us puppeteers have a specific set of rules we have to follow in the heat of battle, to make sure that we can work to the best of our abilities. I want you to go and find these rules we have to follow, and simply expand on that rule, and explain it to me. Most of them can be found in the Sasori guidelines. Just one small thing is that I only want you to find the rules which are made for standard characters, and not for specific puppeteers like Sasori.