First off, I have only really experienced a few. My favorite comedians are, in order, John Mulaney, Brian Regan, and Jim Gaffigan. There are a few others I know of, but those three are the only ones I've seen in which I can enjoy the entire show.
John Mulaney is, in my admittedly limited experience, the best comedian. He has a unique stage presence and he tells amazing stories that are hilarious all of the way through, not simply at the end. He will take a story with an amazing finishing punch line, and then turn that joke into a five minute thing with a bunch of intermittent jokes inside. One interesting thing about him is that sometimes his stories have predictable endings, and yet the way he closes up the story still has you cracking up. The biggest thing about him is that he tells stories about his life and his experiences, and he has no problem with laughing at himself along with his audience.
Brian Regan is my go to for recommendations in comedy primarily because it's clean. As far as I can remember, he doesn't cuss at all during his sketches, so his humor is completely kid friendly. I feel pretty confident in saying most children would enjoy his stuff. He tells a lot of stories, too. Some are about his kids, and some about the silly things he experiences and how dumb people are. He also is one of those comedians that makes facial expressions to augment his stories, but he has quite the repertoire of personas when he does this.
Jim Gaffigan is the lowest on my list because he has the lowest (figuratively speaking) sense of humor. It's pretty low brow, talking about food and making fun of people. If nothing else, he has a selection of octaves when going through his jokes, and the voices he uses themselves can be hilarious. I'm relatively certain Jim Gaffigan is a clean-mouthed comedian, too, but as I said his low-brow comedy can only take him so far in my books.
A few other comedians I've experienced very recently (but haven't seen enough of their stuff to really know for sure) weren't really my cup of tea. The three I just saw were Louis C. K., Tig Notaro, and Iliza Shlesinger. None of them were really that enjoyable for me, because they don't really tell nice, consistently funny stories.
Louis C. K. is probably the best of those three, but he is simply so vulgar all of the time that it gets to be too much for me. I can't enjoy something when half of what I'm hearing is cussing.
Tig Notaro is somebody I'd actually be interested to watch more of, because she is so slow and relaxed its simply a different approach to comedy. I'm far more acquainted with the yelling and high energy of humor, so its a bit of a side step when somebody is telling a really funny story slowly and with a straight face.
Ilize Shlesinger I legitimately did not enjoy. I had no qualms with closing Netflix because I knew nothing she was going to say would be funny to me. She's also sort of low brow, like Jim Gaffigan, but shes far too abrasive with her jokes for me to be comfortable. She doesn't really have a "style" I enjoy, it just seems to be "somewhat vulgar jokes and stories".
But of all of these people, the one I would most comfortably recommend to just about anybody is John Mulaney. Now that I think about it, I don't think I know anybody that knows of his stuff that doesn't love him. I know that doesn't say much, given I'm something of a loner, but hey, I do what I can.