Hello, Michimom!
You are asking about the things to look for when buying a used acoustic piano. I will answer your question according to what you are asking first. Then I will give my opinion as to the differences, good things and bad as comparing acoustic pianos to electronic ones.
I am going to give somewhat of a long post here. And, it will also be in two parts. I am not disagreeing with cpalmist's answer above, but am wanting to give a direct answer to your question as well as a second opinion. Since what someone wants in a piano is truly a matter of opinion as well as taste.
When you inquire about a used piano, the first thing that you want to ask is, "Do all of the notes play?" Then, you will want to ask as to "When was the last time that it was tuned?" Then, "Has it been tuned on a regular basis?" By regular basis, I mean preferably once every six months and no less then once a year.
If it has not been tuned for a long time, i.e. years, then that doesn't mean that it can't make it a good prospect for a piano for you. It just means that it will take more in the initial tunings in order for it to possibly be brought up to standard pitch and sound good as being musically in tune. About three times a month, I have someone call me up who wants to get rid of their old piano, either give it away or junk it altogether. I really like to save old instruments. Even if they are over 100 years old, if they have had regular playing and good care, then chances are that they will last for many more decades provided they are given the same treatment of regular playing and good care.
If you have never played, then I would definitely have someone with you to check the instrument over who does play reasonably well. Preferably, this should be a piano tuner/technician. But if not, someone who plays reasonably well will do.
If the piano is reasonably well in tune, then see what the person who is playing it thinks about the touch and the sound.
Aside from the tuning regularity, you perform the following operations and look for the following things:
Play all of the notes. Any buzzing sounds should be noted. Buzzing could be a rib that is loose and vibrating against the soundboard, a bass string's winding that may be coming undone or just something else on the cabinet that is loose or placed in such a way that it may be causing a vibration. If any of the problems exist, then they can be repaired.
Check for any evidence of water stains around the bottom of the piano. If it was stored in a basement, then there may have been a flood that could have caused some internal damage. Or, separation of parts of the outside of the case. These sort of problems usually can be repaired. But, it may not be cost-effective to have them repaired.
Be sure to look at the back of the piano to see if any wood looks like it has been separated from where it originally was supposed to be. Like the above, these sort of problems usually can be repaired. But, it may not be cost-effective to have them repaired.
Check for cracks in the soundboard when you are looking at the back of the piano. If there are cracks, it might not be a problem at all, because most of the sound on the soundboard travels with the crack, not against it. Therefore, cracks in the soundboard really amount to "a hill of beans." That is, unless a rib is loose right on the crack. Then you might have loss of tone and possible vibrations that aren't desirable. Ribs loose against cracks are not hard to repair. Another thing, is if a piano is very old, we expect the soundboard to have cracks in it. If the piano has been in a place where the humidity has been reasonably stable (60% to 65% relative humidity) and has been tuned and maintained on a regular basis as mentioned above, then cracks will develop. This is normal then and a sign that the soundboard had a good crown on it. The crown on a soundboard is part of what contributes to a good tone. Soundboards normally shrink in time. Cracks in soundboards are not all that hard to fix.
Check all of the pedals to see if they all do what they are supposed to do. Most upright pianos have three pedals. For most uprights, this is just to sell the piano. Upright manufacturers are trying to imitate the look of having three pedals as on a grand piano. On a grand piano, the three pedals all have distinct, individual functions that are separate from each other. The first two pedals, on an upright, going from left to right, almost always perform the same function as each other. That is, to make the sound softer. Most pianists rarely use these pedals. It's hard on the hammers to use them anyway. The most important pedal is the one on the right side. It must function properly. How it functions, is when you are playing notes "keys" and holding down this pedal at the same time as playing those notes, then those notes should continue to ring until you release this pedal.
Are all of the keytops there, both on the white and black keys? If not, then these are easily replaced.
How tall the piano is does make a difference. The longer the strings then the more tone and sound you will have. There is as of yet, no real substitute for the sound of a good acoustic piano.
If the piano has a bench that matches the woodwork and color of the rest of the piano, then that is an added plus.
If you do a search for used piano on Google in your location, you just might find one in great condition that someone is willing to give away for free, or at a very reasonable price. You might also check the newspapers or any of those smaller type advertising circulars that don't cost people a bunch of money to put ads in. You will be more likely to get a better deal by finding a used instrument on your own then buying one from a piano or music store.
You don't need professional movers to move a piano unless there are a lot of stairs involved. Moving a grand does require some special techniques and knowledge, though. But, you are asking about moving an upright. I am assuming that you just mean a vertical piano. Renting a U-Haul will do. You could have two really strong guys do the moving or four guys of average strength. It is advisable to have a piano dolly though. The castors on the cabinets or legs on any piano are only for moving the piano away from a wall for dusting. Not for moving the piano any sort of great distance.
What kind of piano you get, whether it be an acoustic or electronic one greatly depends on what you or someone else is going to want to play on it.
I have two grand pianos in my living room. One is a 1906 Chickering Quarter Grand ("Quarter" has nothing to do with it's size). The other is an 1885 Everett Grand with Japanese lions in relief on the sides of the cheeks. I wouldn't trade them for any other pianos. I play electronic instruments also, but will get into discourse concerning those in my next post. As I said in my first statement in this post,
Then I will give my opinion as to the differences, good things and bad as comparing acoustic pianos to electronic ones.
I will also post about brands to look for and those to avoid.
I have been a piano tuner/technician since 1974. I have also been a piano teacher since 1978 as well as a professional pianist for all of my adult life.