Welcome to the forum!
Welcome to the forum! Learning to fly is an excellent feeling. The warm glow of looking at your pilot's license never really fades. Taxi'ing onto the runway, with permission to depart, pushing the throttle forward to take off, no feeling really quite like it. To answer your questions
1. Cost of a basic license
Standard JAR-PPL seem to vary around the country. Approx £6500 up north, to around £8k upwards maybe maxing at around £12k down south and around London. All depending on how much training you need. People learn at different rates. That's not to say some people got bargains cheaper, and you can go to the USA and train cheaper but with the pound weakening it's not quite the bargain basement it was. You also need difference training when you get back.
2. Flying abroad
Depends where you want to fly, most countries have slightly differing rules. If you want to fly from the UK to Netherlands, France, Belgium, Spain etc then you simply file a flight plan, inform Customs & Immigration and off you go.
If you want to fly in the USA, Canada then there are differences and the USA is MUCH more regulated. You'll need difference training, as well as to take some exams and do a medical (I believe) over there. South Africa & Australia are different again. So depending on where you want to fly, the in's and out's of achieving that will vary.
3. Aircraft hire
There are lots of options on this. Simplest is to carry on hiring club aircraft. There are people on the airfield who probably own aircraft and if you've come through the training will rent their aircraft to you. You'll meet other people going through the training, and some of them will go and buy aircraft in the future. So you'll get to know people who have aircraft. Then there is the option to buy a share in something which will require an outlay, a monthly standing charge but will have quite low hourly fly rates will be cheaper. Then there is buying outright.. Depending on how often you want to take an aircraft away, how often you fly, what sort of mission profile you have, will change which route you go. With the recession in full swing though aircraft hire rates seem to be decreasing, as does the price of Avgas (at last).
That's my top line thoughts on it anyway. The other thing is aviation, although seemingly taught and feeling like a science, I think is fully in the "art" category. It is more than possible to argue completely contrary points to the above, and no doubt somebody will come along soon and disagree or agree with some of this. That's just the world of aviation! Welcome aboard!