If you are trying to find a piano for under $1000, just please keep in mind that the piano may need a fair bit of maintenance to get going. Though I have worked on many pianos that end up working out quite nicely with investment in tuning and maintenance, please keep in mind that sometimes people are getting rid of a piano for a reason, and not all of them are salvageable.
Please make sure that you have a good place for the piano in your home (away from baseboard heaters, wood stoves, heat vents/drafts from windows or patio doors). Good climate control will help your tunings to last longer, and protect your piano from damage.
Bigger is usually better. Typically, the longer the piano, the longer the strings (wire), the thinner/more resilient the wire will be, and the better the tone. In many instances, a tall vertical can sound better than a small grand. At risk of confusing you, I must add that this can vary widely from brand to brand, and has to do with the way the instrument is built and its inharmonicity. Please review the "Piano Buyer" website for further clarification.
Also take into consideration that you will need to pay to have the piano moved into your home. If you need a piano mover, I recommend contacting Northern Piano Moving. If you plan to move it by yourself, please take the time to use a moving dolly, or at least prop the piano up off of it's casters when it's in the moving truck. This extra precaution can prevent a costly repair.
Private sales are risky. Please have a professional evaluation before purchase! Do you have someone musical in your family, or a friend who you can take with you to play some pianos and make educated comparisons? Take them with you when you look at pianos. When you find something that you like, please have me, or another qualified piano technician go to look at it first (or at least call and inquire if I've already tuned the piano). It can save you a lot of future hassle.
Some good questions to ask when you are buying used from a private sale:
1. Who is your piano technician?/When was the last time you had the piano tuned?
2. Do you know the Brand/Model/Serial number? Do you have any service records?
3. Why are you getting rid of the piano?
Every used piano should be judged on an individual basis. Even relatively new pianos can have problems that may not be obvious at first glance. How the piano has been kept over time and manufacturing quality is key. A 100 year old tall vertical (upright) can be better than a small cheap piano made in the 1960's. Heck, it can be better than a cheap piano made in the 1990's! It is VERY individual. Pianos can also be rebuilt and restored, which extends their longevity. Sometimes it can be to your advantage to buy a piano that is more than 10 years old (as long as it has been tuned and serviced during those years). A new piano needs several tunings to become stable, and will also need some "preparation" which can involve maintenance, alignment and voicing.