After the piano, the drum kit represents the biggest investment for the first time buyer, the common kit comprising of 5 pieces: kick drum, snare drum and 3 toms usually including a floor tom, and then there's the 'hi-hat' and other cymbals, stand and pedals etc. It is the standard backing instrument in many genres of music including rock, soul, jazz and latin, and together with the bass guitar makes up the 'rhythm section'. If choosing the drums, make sure that your circumstances allow you the opportunity to practise and play with other musicians, as playing drums only by yourself is not so much fun! Drum kits start from around £300, and will often include the necessary stands, pedals and cymbals, but do check! Playing cymbals wears out sticks quickly, so it's a good idea to buy several pairs (5A is a good weight to start with), and if you plan to move your kit around, you will need a set of cases.
The drum kit is the loudest of all instruments. Although the sound can be damped somewhat by using practise pads that are placed over the drumheads and around the cymbals, it will still be a lot noisier than a flute! Alternatives to damping are the electronic drum kit, which can be used with headphones, and practise-specific 'rhythm coach' pads. Keep in mind though that you will need to play an acoustic kit at least part of the time if you want to develop the best technique.