What do I need to get started with American style Barbecue?
My recommendations would be as follows. 

First, buy a cooker that will do everything you need, but is priced reasonably. You will want something that fits the following criteria:


Provides direct grilling capabilities.
Convects heat fairly evenly, so that you can use it for low-temperature, long-time, indirect-heat cooking (what most people in the US would consider barbecue).
Has the capability to control temperatures easily.
Has plenty of cooking area.


The basic Weber 22.5" (57cm) kettle grill fits all these needs, on a modest budget at that. You can set it up for high heat grilling, low heat barbecue, and just about anything in between, just by how you arrange your fuel. When you close the lid and arrange all your fuel to one side of the chamber, the parts of the chamber that are not over the fire heat very evenly, allowing you to cook things like pulled pork and brisket. The vents make it easy to control temperature by limiting or expanding the flow of oxygen to your fuel. Finally, there are numerous after-market accessories available to if you decide you want to expand your horizons, such as cast iron grates, pizza stones, inserts that make your grill into a pizza oven, etc. So you can start off with a small investment, and then build on piecemeal with accessories. I would recommend the 57cm model, as the 47cm one makes it difficult to cook with indirect heat. Link here: http://www.weberbbq.co.uk/product/one-touch-original/

Once you have your tools, make these sites your bibles:


http://tvwbb.com/
http://amazingribs.com/


Both are full of great information for making good food on the grill.

This is exactly how I got started. Eventually, after I felt proficient enough with my Weber grill, I purchased their Smokey Mountain smoker, as well as a couple of additional grills. It's become an obsession, and one that I have been able to get into fairly cheaply.