I put the strap on first under my sling. That's just me though. I've always used the pram more than the sling, so I wanted one that went easily onto the pram.
A back pack one can still sit in the storage compartment under your pram. It won't be as easy to get to, but shouldn't make too much of a difference.
Mine is a 'Baby Gear' sports style bag. You can get them in back packs too. I recommend them! Mine has 2 insulated pockets. Wet bag, change bag, & about a million pockets!
I don't know what the back pack one is like though. I think it's smaller, but mine was good coz it was big enough for jumpers for us all, over night stays for the older kids etc..