Beer kits are vastly different today compared to the awful offerings available in the "heyday" of home brewing in the 70s and 80s. There are a huge number of kits available today which will produce very drinkable beer which don't have any of the cidery tones of yesteryear. The big difference nowadays is the quality of the malt extract and yeast in the kits, plus the fact that beer is no longer brewed in an airing cupboard.
Wilkinsons is a great place to source home brew kits and basic equipment for home brewing. The 3kg kits such as Woodfordes are a good starting point.
I started brewing kits again 5 years ago, then quickly switched to all-grain brewing. I'm not a prolific brewer, but have brewed approximately 2500 pints of all-grain beer since then. For my brewing vessels, I use heater elements from Asda value kettles, which cost a fiver, plastic 33L fermentation buckets from my local home brew shop, with tank connectors and ball valves from screw-fix. Aquarium heater elements offer very accurate but cheap temperature control. My entire set-up cost about £60. If you can resist the temptation to go "shiny" as mentioned in previous posts, its a very cheap way of producing excellent beer - £10 for 25 litres.
A 25kg sack of grain (which will yield 250 pints of premium strength beer) can be sourced for £25-£30 delivered. There are a range of spectacular American hops available in the UK at approx £5 per 100g (enough for 2-3 brews) which will pack a real flavour-punch in your beer.
This web site hosts a comprehensive beginner's guide to all grain brewing.
For kit and all-grain brewing advice
Jim's beer kit and
The home brew forum are British-based forums with tons of useful information and very helpful forum members.
The only down-side to all-grain brewing is the amount of time it takes to prepare a brew - 6 hours from start to finish in my case, plus time for bottling and sterilising. Some may consider the construction and use of a diy boiler hazardous, though I have never had any problems.
Whichever route you take to brewing, I'm sure you will enjoy the end product. If I can give you any more advice or answer any questions, please feel free to PM me.
Edit: Just read Jeltz's post, The Craft Brewing Association web site looks pretty good and very much like the old home brew forum site.