Your first mistake is a common one...:) You are comparing your child to another kid! There is no other child like your own, and the very first habit to get out of is comparing your child to any other child--each one is different, and each one learns in their own way and at their own pace...and yes!! It is HARD not to compare! :) Common!!
Second--I would say if she is even choking with the water that she is just eating and drinking too fast..:) very common at this age, as well. She is just learning. The fact that she is choking is a good sign....now don't take that the wrong way!! It just means that the airway is working properly, and not allowing the food to get stuck and nature is working to help her learn to slow down and how to eat. :) The sippy cup may also be dumping water out too fast for her to swallow, and you may want to try a cup with smaller holes or one that pours slower...but keep up with the cup! This is an awesome achievement and you should be very proud of her!
The puffs melt in the child's mouth, and are not a "true" solid, per se, but an awesome 1st food to learn from. If you feel she is choking too much, just give her one at a time, forcing her to slow down, get coordinated to eat and helping her learn. Most kids do not get the whole solid food thing down pat until 1 year or later...:)
I would say you are doing great! Most of all--listen to only one thing--your gut--because more often than not, your gut is right. If YOU feel it is too soon, hold back..if you feel that it is more of a learning curve and with practice, she will improve--then keep feeding it to her. YOU are the best judge of what is best. You will always get a ton of advice--but I would say to trust your gut, and chances are, you will do awesome! :)