Disclaimer: I don't live in any of the places but do live and work in the area. I'm sure someone who does live there will be along in a mo, but...
Ricky: nice little town. Mostly residential, has a lot of coffee shops and restaurants, the best artisan bakery for miles, has Met and Chiltern line links to London, schools seems pretty good. There is a well-organised breakfast and after school club which works across several primary schools and also runs a holiday scheme. It's in the middle of a very large cluster of independent schools too, both co-ed and single-sex and for secondary state schools, there's a large Catholic secondary, St Clement Danes up at Chorleywood (lots of buses!) and Harefield Academy.
It has a large Waitrose, a M&S Simply Food and a medium-sized Tesco. It's got canals, the Aquadrome, lots of little shops and a very annoying one-way system. Bit spread out.
Chorleywood: Also lovely, has the railway lines running through it too. Rather hillier than Ricky, is much smaller/compact and only has a few small shops. Does have several state primaries, and catchment for similar secondaries as Ricky. Pricier.
Amersham: has two sections. Old Amersham very old, has boutique shops and a monster Tesco. Amersham on the Hill has the station and a lot of standard high street shops such as Boots and Halfords and Starbucks etc. Sort of half-way between Chorleywood and Ricky really. Built in and around open country and woods, it's got a more country feel and has some extremely good state schools (Elangeni, Dr Challoners Grammar) and also several local indies (Beacon, Heatherton House are nearest)
good luck!