Licences
There seems to be a variety of opinions on what the Wireless Telegraphy Act says. My licences (various) are old, but they all include the wording quoted by PPRuNe Dispatcher.
The reality remains that if you are listening to aircraft comms as a way to improve your skills as a pilot using the radio (and nothing else), you are not likely to be prosecuted. If anyone even knew you were doing it.
Receivers
There are three ways these things tune:
1. Continuous tuning, with a pointer display like your average broadcast portable. Useless for airband.
2. Continuous but with digital readout. Useable but you need one with fine enough tuning to select the frequency you want. I've seen some that jumped in large increments and were useless.
3. Proper "dial in the frequency" digital (ie synthesised). This is what you want. If you can get one for under £100, that's excellent.
I've not used anything under £100 that I know would do the job, but looking at the wsplc website, the Maycom AR108 and FR100 and the Yupiteru look like 3. above, the Steepletones look like 2. above.
The Yupiteru I know, and it will certainly do the job.
Good luck, whichever way you go. Personally, I'd go for second hand (provided you get a good deal).