Well you are on the right track not doing an integrated and first doing the PPL. The cost you quoted is good but take into account that airport fees, books, headset, general ground school equipment, etc. will likely not be included in the cost.
You will definitely stand out compared to other candidates as it shows you are determined and motivated.
And in the case that you do your PPL and decide not to make it a profession but just a hobby, it will look nice on your CV applying to other (non aviation) jobs. Because, well, it stands out. If you are not determined, dedicated and motivated, getting a PPL is near to impossible.
I was in University and after the first year I decided to drop out to basically do what you're doing. I had the exact same mentality. I wanted to go to the airlines. I was 18. No one was able to fund me the PPL so I worked and worked and saved every penny for my PPL. Doing my PPL was one of the best experiences I've had. I loved every aspect of it. For the first time in my life, studying was actually fun haha.
Nearer to the end of my course it got me thinking if I actually want to make this a job. Making it a job would take the fun and pleasure of flying away and the way I felt about flying would completely change. I decided to go back to University and get a degree and just keep this as a hobby.
Obviously you may come out with a completely different mentality. Thought I would share my story because you remind me of my 17 year old self!