You may be lucky enough to have a piano already, but if not you do not have to spend a fortune. You will need an instrument to practice on; practice is as important, if not more so than the lessons.
Electric or acoustic?
Electric
The basics – you will need a full size weighted hammer action keyboard with pedals, on a stand, and a stool (better still an adjustable stool). Deals can be had from £300 upwards. Some include the stool and headphones. Buying a piano is a bit like buying a car, there are pianos to suit every pocket. Generally (up to a point) you pay more for better quality instruments, but like a car, you wouldn’t buy a Ferrari to pass your driving test! There are many electric pianos on the market which should last a long time. They have the advantage of headphones for quiet practice and do not need tuning.
Acoustic
In general, and for the higher grades, I believe that you cannot beat an acoustic piano; no headphones of course, and they do need regular tuning (I can recommend an excellent piano tuner if needed). Acoustic pianos are also like cars, there are many at sensible prices, but the sky is the limit. Many good music shops sell reconditioned pianos which can be more affordable. Perhaps you can treat yourself to a £150,000 Steinway after your first recording contract! (or then again, perhaps not, pianos are very individual instruments and certain makes are more pleasing to some people than others).
Best of both worlds – acoustic and digital
Yamaha have a range of pianos which are both acoustic and electric which can be played as normal acoustic pianos but have the facility of a digital mode for silent practice. One of my adult pupils has one and is over the moon with it.

The piano.