Piano vs. Keyboard
Nothing compares to a piano. However, a keyboard is understandable if you have sound restraints, space issues, or for mobility (I doubt Ben Folds was schlepping a Steinway Grand when he first started playing shows). A keyboard can not simulate all the intricate movements of a piano that create so many nuances- there are over 300 ways to manipulate the pedal for example - and the closer the keyboard is to a piano, the closer the price is to a real piano. With that in mind here my recommendations for a piano or a keyboard:
There is no perfect piano for everyone. I would suggest looking around, even going to refurbished piano stores like Keys 4/4 Kids in St. Paul or Ackerman's Piano in Lakeville. Test each key, make sure the pedals work, probably don't want chipped keys. Play the piano, does it sound good? Does it feel good? That's a good piano.
If you are certain on a keyboard, it is important it has the following things:
1. The number of keys: If you're willing to pay for lessons, then you need to invest in a keyboard with at least 61 keys. 66 or 88 is more preferable. Especially if the student is motivated and wanting to learn, you will end up buying a full keyboard in the end.
2. Weighted keys: In full size keyboards, this is a given for newer models. If you are getting a hand-me-down or buying used, this is something to look for. Weighted keys helps build the student's dexterity. Without weighted keys, they will have trouble performing on pianos and keyboards with weighted keys (during a recital for example).
3. Stand and Bench: No matter what, make sure that you have an adjustable bench and a sturdy stand for your keyboard. I have found students without proper benches do not practice often and pretty much loathe approaching the instrument. If you have a keyboard, there needs to be a place for music to properly sit. This may require buying a heavy duty music stand. (Piano books can get thick)
While all of this doesn't guarantee a happily practicing and successful student, it does give them more of a chance.