I think it is pretty well standard procedure that the first item to be actioned on lift off is 'positive climb-gear up'. It reduces drag and will only be forgotten if you don't do it straight away and get it out of the way. It is advisable to get the aeroplane climbing away at safe speed bearing in mind terrain before anything else is done. Taking it slow, both pilots positively identify the engine and problem followed by Handling pilot calling Fire checklist, and non-handler actioning it. Then you have flap clean-up and conversing with ATC and decision on what to do next. You lose points if the gear is still down at that stage, so very important to do that first of all.
As for roll rate, I have never heard of a minimum or maximum figure. You just roll comfortably into the turn at your own rate.