Limiting job opportunities? Two of my friends fly for DY and SK. Both took a modular route. I also know plenty of others who have jobs via the modular route.
But doing an integrated route will typically make it easier for networking etc. Integrated is also easier for you as a student all in all. I had to do a modular route due to family and work obligations, so I had to figure out alot on my own, especially since I did FAA first.
If money is an issue, you will typically be better of on a modular route. If you got decent skills at networking and you dont give up, you will make it in the end, no matter the route tou choose. I know of people who had to go 6-7 yrs and more until they landed their first proper job. So if you have patience, you will be fine.