Firstly, why integrated?
You mention airlines in Ireland, Canada and the US - they all require different licences, not to mention the right to live and work there. Making the wild assumption that you can work in the US - an integrated EASA course is definitely NOT the thing to do - you can get an FAA licence for a third of the price in a third of the time.
The unwritten rule is you accept the first job you're offered because it may be your last. You might get lucky and go straight to a 737, or you could end up on a king air - then it's a lot more stepping stones to get where you want to be.
Lifestyle is very important: just because you want long haul now doesn't mean you will in 5 years. If you get a wife and kids you'll probably want to sleep in your own bed every night, which means short haul. Of course you might hate the bitch and want to go long haul even more.
The most important lesson in aviation is that things change. Economies change, plans change and whatever you plan now probably won't happen, trust me!
The name of the game for most is to get a command. Command means hours. That means going to an airline that flies you 900 hours a year. Great as an FO, **** as a Captain. Flying 300 hours a year is a great place to be a captain, but **** for an FO looking to become one!