First time passes do count for alot, especially in flight tests such as the IR. So should you not think about where can you get the best training to get your first time passes? Not saying you should go to the most expensive school with the biggest name. I chose to get my ATPL groundschool from a school which specalised in this. Also I chose to do my IR at a school local to me with an excellent reputation. By going down the modular route you should not restrict yourself to one organisation as there might be better options for you.
So far I dont think anyone in recruitment has cared much about where I trainied, but having first time passes in my flying has helped. Also in interviews I have been asked about the decisions I made during my training and could justify them with logical arguments. Only had 2 interviews and been successful in both.
Best of luck with your decisions