Set a Budget
Decide how much you want to spend on your piano. Remember that a good piano will last a very long time so although it may seem like a lot of money initially, over the period of usage it is very little. It's best to get the best piano that you can afford as a low quality instrument will hinder progress.
Grand vs. Upright:
Have you got room for a grand?
A baby grand takes up not much more room than an upright piano, the width is the same but a very small grand will only have two to three feet more depth than an upright. The term "Baby Grand" means any grand piano less than 6 Ft. long, terms such as 'boudoir' 'concert', 'drawing room' grand are not really used any more, grand pianos are referred to by length.
Is a grand better than an upright ?
Grand pianos generally have a better action than an upright piano. This is because in a grand gravity helps the hammers to return when a key is released whereas in an upright this is achieved with springs - which add extra resistance to the action and can lead to an uneven response over time.
Some small grand pianos (4'6 and below) made up to around 1938 have a 'Jack Action' this is inferior to the 'Roller' action. If you want a grand as a serious instrument avoid jack action pianos. Many older Bluthner pianos have the 'Bluthner Patent Action' which looks similar to the jack action described above but is a far superior mechanism and in many ways as good as a roller action.
Generally a large upright piano (118 cm. and above) will have a better tone than a baby grand. Many baby grands are built more as furniture pieces than quality instruments. Beware an instrument less than 5 Ft. 8 in.
Attractive Casework vs. Good Tone
Decide whether a fancy casework or a good tone is more important to you. Do you want the piano as furniture or as a well performing instrument? Usually the fancier the casework the older the piano, and the older the piano the more wear and tear and the more primitive the action will be, ergo nice casework = poor quality instrument. This is not always the case as some 100 year old name pianos are good instruments and also have an attractive casework. I find that many Schedimayer pianos made around 1895 have lovely caseworks and are also good pianos.
Small baby grand pianos (4'6") tend to be better as furniture than performance instruments.
Private vs. Dealer
If buying privately - always get the piano checked out by a reputable technician unless you are very confident in your ability to spot a dud. As a rule if the casework looks bad the insides will not have been well looked after.
Many pianos available privately are pre World War One wrecks and should really be scrapped. If when you view a piano you look inside and it is very dirty and dusty and is a straight strung piano - avoid like the plague !
Other pianos may well have been neglected. Ask when the piano was last tuned, if it was longer than 10 years leave well alone unless you get it checked out.
It is possible to pick up a bargain privately, something like a 1930s largish overstrung underdamped piano with a reasonable casework for around £100 to £300 is doing well. In a higher price bracket small modern (1960s to current day) pianos can be picked up for between £300 (if you're very lucky) and £1000 secondhand.
You will pay more for a piano if buying from a dealer but generally each piano should have been renovated if not reconditioned or rebuilt. Anything in a dealership for less than around £400 will be interesting sounding firewood...
Make sure that the piano is clean inside, this will indicate whether any work has been done to the piano.
New vs. Second-hand
There is a definite choice to make between convenience and character.
A new piano will give you well over 50 years of use if looked after well and should give no problems. New pianos tend to have sleek modern (small) styling and durable polyester finishes.
A second-hand piano on the other hand will be larger and may need reconditioning (if this has not been done) but may well have a better tone than the modern counterpart. Second-hand pianos tend to have a lot more character and more interesting casework than modern pianos.
Avoid second hand pianos over 80 years old unless they are reconditioned name pianos.
Uprights - things to watch out for - Overstrung
It is preferable to buy an overstrung piano not a straight strung! How to tell: Lift the top lid of the piano you should see the tuning pins at the top of the piano. If the tuning pins are evenly spaced along the pin block and the strings are all parallel and vertical this is a straight strung piano.
If there is a group of tuning pins at the left and a separate group at the right and the strings cross over in a X shape this is an overstrung piano.