Source: I spent 7 years working at one of the major publishing houses.
In a nutshell, it is extremely unlikely that a publishing house will pick up your book without it being submitted through a literary agent. You can always self-publish, but that of course comes with no support or marketing/publicity, so if you're really looking to have a successful book, a major house is the way to go. (Penguin/Random House, Harper Collins, etc) I'd look at comparable books on the market that are written in a way that you like and respect - the agent will almost always be thanked in the credits. Then you can start the query process of reaching out to those agencies - there are plenty of websites that will teach you how to write an effective query letter.
Over the past decade there have been many print on demand (today's equivalent of "self-publishing" that have made the NY Times best seller list and have been hugely successful, so there's that. And the biggest print on demand company, Author House is, in fact, owned by Random House/Penguin, so there's that.
Thanks for all the info and advice. My book subject has numerous friends with published memoirs, so hopefully can get a recommendation from one of them for a literary agent. If that doesn't work, then yes, I will go the self-publishing route.
Wanted to jump in to say that the exception to needing a literary agent is being a celebrity. So your best bet may be to have your subject have the meetings and make the deals him/herself (arranged via his/her management), then you can be the ghostwriter once the book is sold.