The first thing to think about is the size of the piano. For example, think about whether you have space to fit in a sprawling grand, or whether you should be looking at upright models. Obviously there are expensive and less expensive in both categories, but it is crucial firstly to understand your requirements to refine your search.
After you've decided between upright and grand classifications according to your space, you should begin to look at the models themselves. You should ideally opt for a piano with a full sized keyboard, so disregard anything of a small size unless this seems more appropriate for some other reason. Next, look for a piano that is towards the top end of your budget. This will give you some assurances as to the expected quality of the piano, and should allow you to gauge which seem more reliable models.
Next, you should pull up a chair and have a play. Ask the music dealer if he'd allow you to play. This should let you get a feel for the way the piano sits, and to see how it feels in comparison to your playing style. There is no more important feature to consider when buying a piano than how it feels for you. After all, you're the one going to be playing it at the end of the day.
If you are at all in doubt about exactly what you're looking for, you should consider asking advice from the assistant. Usually, their advice will be sufficient to point you in the right direction and lead you to a quality model. Obviously, don't feel pressured into buying, but take on board anything the assistant says. Shop around, and ask at various places about what kind of piano you should be looking for in your price range and specification, and you'll eventually establish a common denominator. Do your homework before you buy, to make sure you find the best value for your money.