So, is it worth buying your own ac, will it be a lot more expensive? Surely being able to fly whenever wherever you want makes it worth it?
Also, is the modular route PPL -> CPL -> ATPL? Does hours in a small ac count towards ATPL or do you need something bigger?
You can only fly whenever/wherever you want when you have a licence so by then you will already have say 60 hours. If you want to go commercial then you are going to need an IR and a CPL as a start point. Now you need a multiengine aeroplane for the IR and at least a complex aeroplane for some of the CPL course so your own aeroplane may not fit the bill unless you intend to buy an IR equipped twin with the associated costs. In any event you would need to purchase a well equipped aeroplane to get any real value out of it. In case you haven't noticed, the equipment can cost more than the aircraft!
If you can afford to buy an aeroplane and fly lots of hours in it, go right ahead, but it isn't really going to help you get an ATPL any quicker or cheaper. If you have that sort of money to spare, then why not enrol on the best commercial course you can find. That way you have more chance of earning money at the end of it. Typically to run a light aircraft economically, you need to fly it at least 200 hours a year. 150 of those hours might be useful towards your licence experience.