Now, in answer to the OP's questions:
1) cost - as has been stated,
AFAIK anywhere from probably 7k-12k. Used to be a lot cheaper to do in the US or Spain, but as Sterling heads South.... btw, you do NOT need any additional 'training' if you do your license in the US (or any JAR country, for that matter).
2) any license is valid in the a/c of it's country of registry, worldwide. However, in Europe there is a thing called JAA (Joint Aviation Authorities) that produces a JAA (JAR) license. Confused? OK - here goes: as the UK is a signatory to this process, your UK (or any other JAR) license is valid in any of the other JAA countries. So, you can fly a, say, French registered airplane on your UK JAR license and vice versa. And, of course, you can take your G-reg anywhere in the world
3) Initially renting. Remember: if it floats, flies or f**ks - rent, don' buy! That said, the UK renting scene is rather depressing, so you will most likely want to look for a share or ownership in the future.
4) Knowledge - you are about to embark on a journey of infinte learning, which, IMHO, is one of the beautiful things about aviation. There simply is no point where you 'know it all'. In fact,as you will find out, the more you know, the more you know you don't know.
Keep asking and welcome to Pprune!