We have a young family friend, who wanted to make some short outdoor interview type videos, so needed one of those "cordless hand held mics, like they use on TV" as he put it.
On my side of the pond they only use radios on the mics if they have to. Most interviews by my local broadcast stations are made with a standard reporters mic (in this case, all my local stations are using Electro-Voice RE50N/D-B mics, I imagine that on your side of the pond they are mostly using Sennheiser MD-42) using a short XLR cable going back to camera.
The pros tend to use radios only as a last resort. That's because they know that nothing beats a $20 USD XLR cable. Radios are orders of magnitude more expensive, much less reliable, more difficult to setup and maintain, and the biggie -- radios sound worse. Even the most expensive radios don't sound as good as a $20 cable.
Save the radios for those occasions when there's no other way to get the job done. That's what the pros actually do.
If your young friend is adamant (and what teen doesn't know more than any adult?), the Sennheiser SKP 100 G3 Plug-On Transmitter is the cheapest I'm willing to use myself. Note that this transmitter does not supply phantom power, so it's only good for dynamic mics (like the two I've already mentioned). If you need phantom, you need the SKP 300 G3.
EDIT: And you'll need a receiver too. Either transmitter will work with an EK 100 G3 receiver (as long as transmitter and receiver use the same frequency bands).
That said, there are a couple of new systems that are basically cordless telephones. Audio Technica System 10 comes to mind. Rode makes something similar. Both use the 2.4 GHz band and frequency hop like a cordless phone. The AT system 10 has gotten some good reviews, but I've got no experience with it, nor does anyone I know.