Buying a piano or keyboard can be a bit of a nightmare. The first question is, 'Do you want a keyboard or a piano?'.
If you want a piano do you want a 'real' acoustic or 'electronic' digital one? Hopefully the advice below can be of some help.

If you want a 'real' piano, take someone who can play with you when you plan to buy it. Pianos can look remarkably beautiful on the outside but be an absolute nightmare inside. They can also sound very different depending on how they have been set up. Some pianos are very quiet, while others are extremely loud. The only way to find out is by playing them. If you have any doubts ask a piano tuner to have a look at it for you before you buy, especially when buying privately.

Because of the improvements over the last 25 years or so, more and more people are buying electronic pianos. These days they tend to have weighted keys so that they not only sound, but feel like playing an acoustic piano. Different manufacturers do this in different ways, but basically it comes down to fully weighted or semi weighted. Fully weighted is the best option as it is the most realistic but semi weighted pianos can be slightly cheaper. Another innovation is what's called 'progressive hammer action'. This makes the keys at the top end of the piano lighter to play than those at the bottom end to make it feel more realistic. The best thing to do is to try before you buy.

Yes, you can now buy a silent piano. It is actually a hybrid, an acoustic piano that is also fitted with a digital piano. I believe that they work really well. In normal use the piano uses the hammers and strings of the acoustic piano, but when you plug in headphones it switches to the digital one bypassing the strings. These are ideal if you are conscious of disturbing others when playing, especially late at night. The system can also be fitted to an existing piano. 

For keyboards I would recommend buying a reputable make. How much you spend is entirely up to you. You need to be sure that the keys are fullsize - please don't buy one with small keys, even little fingers find them difficult to use. Preferably buy one with a 5 octave keyboard, which most do these days and avoid ones with lots of gimmicks such as light up keys. Your main goal is to learn to play it rather than trying to keep up with flashing lights or sitting listening to the wonderful demo.