It's clear you have a lot of questions which is perfectly natural. I have a few thoughts:
- Get a class one certificate before anything else.
- Don't be lured in by a big name or by good marketing. Go visit any school you're interested in and check it out. Ask current students out of earshot about how strongly they'd recommend the school.
- Pay as little as possible in advance. Certainly don't pay big deposits or up-front course fees. Combined with this, give yourself flexibility. What happens if you go to school X and don't like it? Integrated gives little flexibility whilst modular gives a lot more. Modular is also cheaper. It's a no brainer.
- I would also strongly recommend getting dual UK CAA and EASA fATPL if possible. The cost increase isn't that much over doing one or the other. You simply need to the ATPL theory course, CPL/IR course, and APS or MCC at dual registered ATOs. Though note you do have to do each ATPL exam twice and the CPL/IR skills test twice (once in the UK and once in EASA land). I'm sure someone else will know the finer details.
What I would do if I were you is to first get a class one medical. Then go to a reputable local flight school to do your PPL. Remember to visit and speak to other students if possible. Oh, and try to pay as you go. Tell your FI that your aim is to fly commercially so you want them to be consistent on SOPs and procedures to keep you on your toes.