You are correct with the ages, 16 for solo and 17 for issue of the licence. If you do start at the age of 15, it would probably be better to start closer to your 16th birthday, as if you fly regularly, it may not take that long before you are ready for your first solo. There are options out there to complete a PPL in a few weeks, but there are no guarantees that you will actually be able to complete it in this time (the weather being a major factor in many cases), also if you do try to complete an intensive course it is worth considering the ground school exams, and have them completed before you start....If you are interested, there is no reason why you can’t start some reading now!
With regards to different schools and prices, a simple web search will act as a good starting point. There have also been many threads on this website surrounding flying schools and people’s experiences, so the search function is another good place to start.