You can spend a FORTUNE on a piano; or you can spend much less. There are many used pianos out there and some used organs, some of which could be obtained for hauling them away.
I have played the piano and organ since 1960. I don"t claim to be super at playing either one, but I do enjoy amusing myself with them. When I am playing, I am somewhere else, a place that is mine only. I have spent many, many hours that way doing something I love to do. On the other hand, I do NOT enjoy performing at all.
Your post says your daughter is 13, which probably means she is in the 7th or 8th grade. It was about that age that I made most of my musical progress: I got able to play almost anything my teacher wanted me to. But it took hours and hours of dedicated practice for me to perfect difficult works. And I didn"t enjoy performing then either.
But then came High School. There were more things to do, including lots more homework and lots more socializing, as well as a bus ride to and from school. I also had lots of chores on the farm all the time. My time at the piano suffered, and my music progressed much more slowly. I also discovered rock and popular music, which was a whole lot easier to play, and started playing music with some of my friends.
And then came my driver"s license when I was 16. I did not continue lessons after I could drive, since I felt I was too busy, had not progressed much in a couple of years, and decided I HATED performing in public. I was never going to be a concert pianist and the few times I played at church were extremely stressful for me, even though people said I did a good job.
The piano I started with, and still have is a very old Kimball upright grand. My grandfather bought it in the 1920"s after plunking on lots of pianos in used piano stores in the nearby town. He liked the sound and action of the Kimball the best of the ones he could afford, and after selling his wheat crop, brought the Kimball home. Unfortunately none of his children learned to play it, and my Mom, the only girl in the family ended up with it. My parents realized I had some musical talent and gave me lessons, even when they were pretty poor. That was a great gift!
My old piano is not beautiful as a piece of furniture, as it has been moved many times and is well over 100 years old. It probably has a fair market value of $100, but it is one of my prized possessions and is one of the LAST things I would ever give up. It is very heavy and is a real pain to move. The next time I have to move it more than a few feet, I think I will employ a piano moving company. But that old piano is one of my greatest sources of personal joy.
Over the years, I have been given several older organs. The largest and best one was my piano teacher"s practice organ. She was also our church"s organist for more than 50 years. When she died, her daughter tried to sell the late 70"s organ, but found that no one wanted to give her anything for it. So she gave it to me. I don"t claim to be a very good organist, but I have had some fun with it and the other smaller spinet organs I have been given. At this point, I should probably become and organ donor, at least according to my wife.
Playing the piano and the organ are related, but really not the same. Playing the organ correctly involves using the low tone pedals, which is a skill set that I certainly have not mastered. I know people who are really good at playing the organ, but they are few and far between. It, like so many things, takes lots and lots of practice.
Getting back to your question about what kind of piano to get, I would suggest taking your daughter along to look at some used pianos and have her try playing them. In my experience, some pianos (and organs) are much easier to play and sound much better than others. I do not care for the actions of lots of spinet pianos I have tried. Most, but not all of the grand pianos I have played had nice actions and have wonderful sound. But my favorite piano is the old, familiar upright grand that I have had most of my life.
Other things I would consider are the space you have to put the piano in and how much you want to spend. A piano should be in a spot where the temperature and humidity are quite constant. If it is an upright model, it should be on an inside wall. A grand piano, of the various sizes takes lots of room, as there should be space all around it, and you should be able to open the top for good sound. Pianos can be as cheap as free to as expensive as you could imagine. There are many pretty good used pianos that look nice, play well and sound good for $1000 or less. There are also wonderful new pianos available, but they cost much more. Perfectly good older organs are often free or almost free, if you ask around. Lots of churches no longer are using their older electronic organs.
And then there are the various keyboards. I would not suggest a cheap one for a couple of hundred dollars. My experience is that they don"t feel right and while they are fun, they really are not that good for practicing on. Some schools have had electrified pianos that had decent actions and were OK for practice pianos. Occasionally they are for sale fairly inexpensively. I like the feel and sound of the church"s Clavinova, but I think it cost about $8k 10 or 12 years ago.
If my middle school aged child was asked to play for church (and I didn"t already have a piano), I would try to find a somewhat similar instrument to what the church has for her to practice on, but not something that I had to spend a lot of money on. After some time, she will decide if she enjoys playing in public. And she might even get paid for playing. On the other hand, after a couple of years, she may not want to do it anymore, because she things she is too busy with other things in her life to do the necessary practice, or because she, like me, really does not enjoy performing.
I am glad to read that your daughter is learning to play the piano. That is a gift from you to her that she may enjoy the rest of her life. Making music is truly one of my greatest joys! Good luck.