This is sincerely up to you.
If you want to get your frozen atpl asap, then go integrated.
If you want to have you own schedule, do it modular.
There are lots of trainee programs where you do your initial flight training and then go on to turboprops or even jets.
Netjets (not sure if it's still open) and Gapan (now closed I believe) has recently launched such a scheme.
Maybe it's something for you too and you need not worry about this type rating business.
Have you looked at CTC and FlyBe?