As a bit of an aside, I always go:
Rotate (10 degrees)
Make sure the beta target is centred and we're flying where we should be (no emergency turn etc.)
Trim
Autopilot
TOGA
Works for me.
I can't really think of any reason why you wouldn't want to use TOGA? Controllability wise I generally wait until it's flying away safely before giving it the extra.
I believe Monarch SOPs stipulate PNF to give TOGA thrust as soon as an engine has failed?