It's been several years, but we spent several months researching/shopping for piano for DD who was about 8 at the time. We ended up with a Yamaha U1, widely reported as a great entry-level, will hold it's value, will last a long time, etc., quality piano. There are cheaper Chinese-made pianos, low-end instruments that can't be maintained/repaired over time, etc., but a near unanimous message from research was to get something that will last. They are easier to play, more enjoyable to play, etc., while cheaper units will turn off a student who can't get good sound/play-ability out of it. Unfortunately, ours was $2,500, and that was a late 1990's model (which our tuner tells us was the best era for Yamahas), and was a decent deal based on the market we saw.
I suppose this is the same as any instrument - she had a cheap rental flute through school for a couple of years until she decided she wanted to continue with it. We invested in a quality flute (also a Yamaha), and she finds it much easier and enjoyable to play. From some quick poking around, both Yamaha instruments sell today for same/more than we paid, where her rental flute can be found for $50 on Ebay.
A piano is obviously more challenging to buy cheap/short term and then invest/buy-up later, due to the size/cost of moving/delivery/etc. If you think she's serious about a multi-year effort to learn, I'd invest in a quality unit, if possible.
