Is An Old Piano Better Than a New One?
There is no easy answer to that question. There are wonderful old pianos in good condition, which will afford you many happy years of music, and there are terrible old pianos which will produce broken parts every time you think you just fixed the last broken part. Pianos which were built well years ago, and have been properly taken care of by their owners (or simply endured well under adverse circumstances) are a great value, and are generally gobbled up quickly when they are put up for sale. Some of those pianos are sold privately by individuals and others are taken in on trade-in by piano stores. Only a knowledgeable piano technician will know a good instrument from a bad one.
Some piano stores take in old pianos, rebuild them beautifully (both inside and out), and put them up for sale. Those tend to be very good values. Other stores take them on trade in, clean them up with some furniture polish, do absolutely nothing to restore the internal mechanisms of the instrument, and proceed to advertise and sell them as restored instruments. Some of those instruments have spent twenty years in somebody's dank basement, collecting mold and rust, and allowing the pin blocks to rot, where the piano can no longer hold a tune.
Be aware that the condition of the cabinet ( the furniture of the piano) has nothing to do with the condition of the inside (the parts which must work properly in order to produce music).
Also, realize that if someone offers you an old piano either for free, or for next to nothing, you will still have to pay someone to transport it. You cannot pick up a piano and carry it, or throw it in the trunk of your car. An old piano which is in poor condition, will probably arrive at its destination with broken parts. It may cost you more to replace those parts than you paid for the piano.
Is a Grand Piano Better Than a Vertical One?
Again, there is no simple answer. There are grand pianos that are built better and sound better than verticals, and there are verticals that produce better tone quality than some grands. Tone quality (which is partly a matter of taste) is determined by so many factors that piano manufacturers are regularly disputing the issue. Generally speaking, a piano with a larger soundboard and longer strings will produce a fuller tone, but not always. A multitude of factors influence a piano's tone. Essentially, as a consumer, you have to listen to different pianos and decide which sound you prefer.