Awesome question which depends on the kid. Generally speaking I'd recommend:
A copy of the Cosmos series to inspire them. I cannot speak highly enough about this series.
Install Stellarium on a computer, it's free. It allows them to learn a phenominal amount about what to look for and doesn't require a dark sky.
A red filter for their torch and a plastic planisphere https://en.wikipedia.org/wiki/Planisphere
Total cost: £20-£30 (UK prices, cheaper in the US)
Take them outside and let them try and identify the constellations using their planisphere. If they're enjoying what they're doing and are engaged after a few nights it's time to invest in a pair of bino's (preferably tripod-mounted though this is not critical). If they get bored you have bino's which are useful for other things or can be sold on. If for some reason they break the binos it's not a big deal. You can pick up binos and a solid tripod second-hand (used) without spending too much. There are specialised astro binoculars, don't worry about those when you're starting. With bino's they'll be able to see a lot of detail on the moon's surface, planets, quite a number of Jupiter and Saturn's moons and some detail in the 'faint fuzzies' (deep sky objects). Celestron SkyMaster Giant 15x70 bino's are a safe bet.
Cost: Potientially as low as £60
If they're still engaged after working with binos for a few months it's time to start thinking about newtownian telescopes. You get far more bang for your buck with these scopes (sensitivity) than a small refractor and there's no chromatic abberation. Of the two mounting options, dobsonian (alt-az) is the most immediately intuitive but if you're willing to put a little time in, a manual german equatorial mount or GEM makes tracking objects a lot easier. Aim for around 4 inches of aperture. A Celestron 127EQ is a great little beginner option.
I'm in danger of looking like I favour Celestron over other manufacturers - this isn't the case. You'll find a fair bit of competition in the low-end of the telescope market so Skywatcher, Meade, Celestron, Orion and GSO are all good manufacturers. As with everything, read the reviews before buying.