The most important thing to decide first is whether to buy a traditional acoustic piano, or a digital one. If you have several thousands of pounds burning a hole in your pocket and an empty corner in your vast lounge, then an acoustic grand piano would look and sound absolutely wonderful. However, for those of us living in the real world, the best solution is neither easy or obvious.
The two main considerations are cost and space. Even a baby grand piano takes up a large amount of room and an upright piano is still quite a large piece of furniture to accommodate. Costs are more complicated - especially when considering the second hand market, but here's my opinion, for what it's worth.
If your budget is less than £1800, then it might be best to opt for a digital piano. Instruments around this price are available with a piano action very similar to that of an acoustic piano and the sound is sampled from a real concert grand. This means that each time you play a note, you are actually hearing the sound of a grand piano. In general, the more you pay for a digital piano, the more realistic it will sound throughout its range at whatever volume you choose.
For more information a sales, try your favourite search engine, or start with these websites for starters:
Models from Roland and Yamaha are readily available, have excellent sound properties and represent very good value for money. A number of other well thought-of manufacturers e.g. Korg and Kawai also make very good instruments, but they are less widely available, making it more difficult to audition them in the flesh. A second hand model that's just a few years old can have an excellent sound and feel for comparatively little outlay.
New acoustic pianos (upright) in this price range are likely to be small and this restricts the length of strings it can accommodate. Trying to produce a rich bass tone from a short string is extremely difficult Most modern pianos are over-strung to increase string length but an upright piano still needs to be quite tall to give a good tone. In order to produce a piano at this price, the manufacturer may have had to cut-back on the quality of materials used leading to poor or uneven tone and/or action.
Buying second hand can produce a bargain, but two phrases spring immediately to mind - 'Caveat emptor' and 'You get what you pay for' (most of the time!).
Basically, when looking at a second hand piano, if you don't know what you're doing, either take someone with you who does (i.e. a piano technician) or prepare to be disappointed. A sticking note or broken string are easy to spot and easy to repair, but if the action needs a complete overhaul, it will not come cheap!
Use the internet to find out other people's views on pianos and the different kinds available. Decide whether you want a digital or acoustic instrument. YouTube can be invaluable here.
Seek out a retailer who sells both (a busy Saturday afternoon is not ideal!). Try them, compare them, don't be afraid to talk to a member of staff - it's what they are there for.
Don't buy one at your first visit, even if there's a special offer you can't refuse.
Are there any suitable reconditioned ones available?
On digital pianos, don't pay for features you are not going to use.
An acoustic piano will need tuning once or twice a year and as it ages, the action is likely to need attention in order to keep it running smoothly.
Do your homework! Find out as much as you can about different pianos both on the internet and in shops/dealers.