I don't see any harm in a coat, it would save drying him off when he comes in!!
If you do try one though don't get a very expensive one, try a cheap one first. I got a coat for my giant breed dog (he is getting on a bit and has arthritis), after the first two or three times he now refuses point blank to wear it!! He hates the rain but would rather go out in the rain than have the coat put on!!! Lucky it only cost 15 pounds!
As regards introducing the pup, if you are collecting him in the car take Alfie along and then just return to the house together. I just act like it is a perfectly normal thing and pup has been here for ever, nothing to make a big deal out of.
I have always used a cage for my pups, it gives the older dog time out from the pup and you can seperate them safely when you cannot supervise them.
Good luck, enjoy your new pup!