Engineering graduates are reputed to be the best paid of all. So, bank the money & save.
Pick your engineering job carefully. Try and get some experience that an aviation employer might see value in. Aeroplanes are technical things now more than ever, so that plays to your strengths. The hot buttons at the moment are CRM and SMS. Something that added experience in those areas might help. You should start with whatever aviation based engineering companies are near you - who knows you might get lucky.
Assuming your engineering degree is mechanical based (vs civil engineering, etc), then you should be able to knock off a couple of CPL exams with very little coaching. I would hope you've done enough human factors in your degree to be able to pass that one straight off. Aerodynamics & Performance shouldn't need much study. I'd get into doing them as fast as possible. You can't log CPL lesson time until you do. Buy some trial exams and see how you go.
If you are serious, I'd run straight into ATPL theory while its still fresh in your mind, but it imposes the discipline that you will get to 1,500 hours within the validity of the exam results (3 years?). Certainly, I'd be trying to do ATPL before you loose too much study discipline.
You'll need to build hours, so finding something like glider tow work on weekends would be a good thing. Anything you can get easily, locally (especially with a new PPL) will require that the organisation know & like you. So, be prepared to "hang around" some organisations you like to build relationships. You need to get to the CPL minimum hours as fast as possible and it doesn't matter what in.
You're going to be learning to fly part time for quite a while. I'd be looking to build a relationship with the most reputable school / instructor you can find. You'll be needing a recommendation or reference from them, so its important to pick someone whose recommendation carries weight. At some point you'll be asking someone to waive minimum time requirements to let you fly something. You need a very solid recommendation from a heavy hitter for that.