dezzy wrote:You could get an electronic kit and headphones

Nah, completely different feel to a proper kit. Practice pads (rubber mats that sit on top of the skin and kill the sound) would help but will kill the feel too, so might as well buy an electronic kit instead of going down that route.
If you get a real kit, get some old carpet (or ask a carpet shop for some old samples) and put a couple of layers under the kit. Put lots of heavy furnishings in the room too (cushions, thick curtains etc). Put a thick blanket like a travel rug or even a single duvet in the bass drum (so when shopping for a kit, get a bass drum with a hole in the front skin to make this easier). If you're really keen to keep the noise down, take the top skins off and put a towel inside the snare and each tom, but that's a pain because you have to retune every time you put them in or take them out. You can stuff a yellow duster into the hi-hat and lay a small towel on each cymbal too. Beyond that, you're stuffed really - it's going to be LOUD.
Do not put gaffer tape on the drum skins and cymbals to dampen them. It's a pig to clean it off again and any solvent will trash the skins (frickin' recording studio sound engineers...) and it'll dampen them a bit but not really get rid of much volume anyway.
Just go for it. Buy a reasonably cheap second hand 5-piece kit and you won't lose much if you need to sell it again next week. If you spend £1000s on a pro kit, it might be harder to shift, but there are always kids looking for cheaper kits so get a simple one until you know you're sticking with it, then trade up.
Also, if you try different styles you can keep the average noise down. You wouldn't play swing/jazz as loud as heavy rock for example.
Plus, initially you will spend most of your practice hours learning rudiments and coordination, and you can do that on a table top or practice pad.
G