My first question would be if she has been tested for CAE, CL and johnes disease. If she is under 6 mo most likely not, then ask about her mom, if she's been tested.
What are you getting her for? If for show or milking, ask about her conformation, her parents as well.
Do you have other goats? You really need to have at least 2 because they are pack animals.
If/when you get serious about buying her, I would actually ask for the paperwork saying she or her parents are disease free... Reason being all mine were "supposed" to be tested, well the lady that helped take the blood owned my standard does a while back and she never had them tested and neither did the people I actually bought them from. Also, if they tell you that she hasn't been tested then you could offer to pay to have it done yourself, that way you are not stuck with a sick animal. I think I paid the lady $15.00 per goat to get them tested, I know it's inexpensive to do so though, and then at least you know you are not getting a sick animal.
Those are just suggestions... I have been fortunate to get my clan tested and they are all disease free, none are registered, 3 could be but they all came from Craigslist, all 8 and 2 sheep, now 2 are expecting
If you care about showing or having registered stock ask if they're registered and make sure you see the registration papers before handing over the money.
And like Janeen, I always like to know the medical history. I think meeting the goat and asking more questions right then and there is always even better. If they're inclined to lie it's harder in person and you can often tell if the goat is well or what's going on.
Ask to see the parents and if you're getting a milker, check the udder on mom, sire and baby.