Well, Ms Sunny Apple. First of all, welcome to PW! It is a good place to find out all kinds of things about pianos and music, and there are some lovely people here who share their knowledge and love for the calling we all share, in some measure.
I would also say, good for you for offering this opportunity to your daughter. It is a very special thing to do this. A lot of people would not make the commitment. My grandmother married into a musical family, and even though she was not musical herself, she bought a used (but nice-looking) piano so her daughter--- my mother--- could learn. She understood the importance of encouraging talent. She learned; I learned; her piano went to my brother, the high-school band director, and I got my own piano. It will be passed down to whoever is bitten by the music bug, who has a stable place to keep it (a grand piano is a commitment in its own right).
Now, about that piano you have your eye on. The advice you've already received is well-taken. Rule Number One when shopping for a used musical instrument: condition is everything. It is fine if it looks presentable to you, and the seller tells you what good care it has had, but neither of you has the training and knowledge of a piano technician. That person will inspect the piano for condition, reading the true story of its life as he (or she--- there are some very fine female techs) looks inside the case.
Among other things, he will be able to tell you what is good, and what is wrong with the instrument, and to give you an estimate of what it might cost to put it in good playing condition. And, an estimate of a fair price in your area. This inspection typically costs in the neighborhood of $100 (there are other levels of estimating that can cost more, for example, producing a written report to be evidence in a court proceeding).
We don't know where you are, so that's about all I can say about it. Now, about finding a piano tech. The best I can tell you is to go the the Piano Technicians Guild website (good information there, too) and use their directory to find a list of qualified techs in your area. http://ptg.org
Ok. The piano. I can't jump through the computer screen and tell you what's what (and I'm not a tech anyway), but going on what you have told us, I would have to say, the indications are not great. Rule of thumb is that pianos of good quality normally have about 50 years of musically useful life, before they need work that is pretty expensive. The Yamaha consumer grade pianos usually don't get a rebuild; people can buy a new one for less than a rebuild costs.
An old piano that has been gently treated and has had regular attention from a pro (like, keeping it in tune, and in good regulation and voice), has a better chance of living beyond 50. Keeping it in a stable environment has a lot to do with it, mainly the relative humidity. Pianos like it to not jump around too much; it does bad things to the action and other parts of the instrument. The Deadly Three environments which destroy pianos: bars, schools, and churches. They are typically beaten to death, given inadequate care, and subjected to violent jumps in temperature and humidity. And, not uncommonly, subjected to acts of vandalism (I count drinks spilled into them, cigs stubbed out on the case, legs broken off when they are carelessly rolled around, tacks driven into the felts on the hammers, etc).
This only repeats what you have already heard from our other members. I am sorry to have to say it. If you are serious about it, make the effort to have a tech inspect it. BTW, you should pay for this yourself. The tech is there to serve your interests, only, and to give you, alone, the real, honest truth. That hundred bucks, or whatever it is, can save you from an ocean of tears. You will be clear-eyed as you continue your search for the right instrument to open up the world of music for your daughter, and for the whole household.
I wish you the best of luck. Please write back as you go through the process; we love these piano search stories, and you can never ask too many questions.