I've only done it as a day trip (3 times) from Suffolk!
I used Ryanair from Stansted to Genoa. BA flies there from Gatwick. There are no other direct scheduled flights from the UK but Thomas Cook have charter flights from Glasgow, Gatwick & Manchester and Thomson has charter flights from Birmingham, Gatwick & Manchester.
There are 25 bus departures per day to Genoa rail station, taking about 30 minutes. The fare is €6.
The coastal rail line has a reasonably frequent service and it's very cheap. (Remember to validate your ticket at the machine by the platform entrance prior to travel).
The resorts along the line are all fairly small and generally upmarket. Santa Margherita Ligure became famous because Elizabeth Taylor and Richard Burton had their holiday home there.
Portofino is the current billionaire's resort. (You can't get to it directly by rail or even by road, as private cars aren't allowed to enter the resort. You need to take a boat from either Santa Margherita or Rapallo or, of course, a bus).
Rapallo is actually a small city but the delightful resort area combines a lovely (if small) beach, with excellent eating places and a wonderful local market.
http://www.independent.co.uk/travel/europe/the-complete-guide-to-the-italian-riviera-1681496.html
http://www.virtualtourist.com/travel/Europe/Italy/Liguria/Santa_Margherita_Ligure-143308/TravelGuide-Santa_Margherita_Ligure.html
http://www.independent.co.uk/travel/portofino-small-but-perfectly-formed-8733812.html
Beyond the main resort towns, the rail line goes on to Cinque Terre
http://www.lonelyplanet.com/italy/cinque-terre
You could probably find accommodation as you went along but it would probably be best to book ahead unless you're particularly adventurous.