I am a great believer in learning at the airport / airfield that you can get to most easily as once you get into it you should be looking to be at the airport up to 4 to 5 days a week, be it a few hours after work for ground school or a quick lesson after work. To drive a liong way to be stuffed by the weather is very boring, apart from the oppurtunity to learn ground school stuff.
With regards buying shares in planes, forget even thinking about this until you have a couple of hundred hours or so - you will know so much more about what you need, want and how to get it.
Most schools will rent you a plane for a day or so (or a week or so), but will probably want a commitment of a reasonable number of hours to justify the plane not being available to them. But the important thing to remember is that you only pay for time in the air (this may be worked out with time to taxi added or charged on a Hobbs meter). Cabair for instance operate in slots of two hours. So if you take the plane last slot the night before, and return it for second slot the next morning you would be reasonably expected to have used it for an hour a slot flying time. An hour will get you over to France or Belgium for the night, although of course you cant enjoy too much wine/beer once there.
If you want to go for longer, look to hire the plane mid week when it is quieter, weekends tend to be premium times. Or what I have done a few times is hire the plane on a Friday afternoon, then returned it the next Friday having put about 22 hours on it - great fun, a weeks trip to Spain, Balerics, South of France etc. The school gets a reasonable return on the plane, and you get to have a lot of fun. Share the flying with a pilot of similar experience, and share the cost. If you swap PIC at every airport, and plan to do similar legth legs each of you logs about the ssame time, roughly half the total. You also both get to put the new airport in your log book.
But I fear all this is way ahead of you - getting the PPL is the first step. See if you can get to know other student pilots of around the same experience as you, then you can compare notes, learn from each other and generally progress together. You might be lucky and your instructor may introduce to you people or you will meet someone on a club trip perhaps. Teaming up will help you learn much faster, and you can all go on trips and share the flying but get twice the experiecne. Once you have this, fly around a bit hopefully with the same person who you learnt with if this worked for you. Get 20 to 25 hours under your belt then think about the IMC. This will be hard work, but teach you loads. It will tighten your flying to such a degree that you wont beleive. It may make your head explode a few time, but once you get it done it is such a fantastic acheivement. Then fairly soon after, perhaps towards this time of year do your night rating. Make sure you go up on and around bonfire nioght, to see the whole of the south east of England sparkling is fantastic - fly from display to display, enjoy!
Once you have this set of qualifications, get flying hours - go places, visit different airports, countries, just go fly. Then see if you want to go commercial. This is a whole new ball game, but you may be best advise to get your PPL and think then.
If you go and fly abroad, to answer your question, the proof of hours flown is recorded in your log book, which you get the instructor to sign every now and then. Also keep detailed receipts from the flying schools as these will be further proof should it be needed ever. If you stick at once school for most lessons they will sign off certain acheivements and the hours flown need to be right for this to happen. So the logbook is the important record here.
Good luck, and enjoy!