Dogs are pack animals and want company. It is kind of mean to separate them from the rest. So, yes, keep the pup with the rest of you. You may have to put a hot water bottle or some such in the crate at night so the poor thing has something warm to cuddle up to and does not feel so alone. I used to think crate training was cruel, but I am all for it now. Remember, straight outside the instant the puppy comes out of the crate. When you are not directly interacting/playing/training the puppy, put him back into the crate until you are sure he is potty trained. Do not set the pup up for failure, always easy success that gets lots of praise.
BTW, if you say the same thing over and over again while the pup is peeing or pooping, you can teach him to go on cue. This will be really handy later when you are in a hurry or traveling to get the dog to go "right now". We use caca.
Enjoy your new family member.