Being a best seller...in perspective:
Technically, I did write a "best-seller" once. It was about how to use a particular piece of software and it sold fast enough to make Number One on the list of record at that time for computer books. So, it was, briefly, the number one selling computer book. I think total sales for that book were 80,000 copies over the first 6 or 7 months. I have had several successful 'literary' writers tell me they have never had a book sell that well. Of course, you can sell screen rights to a literary work a lot easier than you can for a software guide.
Speaking of sales, something to bear in mind, whether you publish yourself or get published, is that books have a somewhat unique place in the retail market because they are shipped to book sellers on a "sale or return" basis. A book store is allowed to return unsold books for full credit. If 10,000 copies of your book ship out in the first six months of publication, 3,000 could come back in the second six months.
While the publisher is going to count initial 'sales' against the advance they may hold some money in reserve in case your books come back. BTW, the publisher will likely want to give you just two statements per year. Insist on quarterly. Even that will mean you won't see any money over and above the advance for some time after publication, IF the book sells well.
How well a book sells is often determined by how many people know the book exists and that is often determined by how much effort the book's publisher--either the publishing company or you if you self-publish—puts behind the book. Publishing operates on small margins and is known for high staff turnover. A not uncommon phenomenon is for the editor who signed up your book to have 'moved on' before it comes to market, or for the publisher to have shifted focus. The enthusiasm you saw when they presented you with the contract has ebbed and although your book is in their catalogue there is nobody 'pushing' it to the big chains and reviewers. Alternatively, the big chains were eager at the outset but now have lost interest.
These are some of the factors that are beyond your control when you sign with a publisher. At least if you know about them you can plan to counter them. Don't bask too long in the glow of signing the contract. Deliver the manuscript as fast as you can and keep in touch with your editor to maintain the buzz.
By now you might be wondering why you would even bother with a major publisher. I know I found myself wondering and I have tried self-publishing. But in fact, there are several very good reasons to publish a book with a major publisher. First is the "authority" factor. Not sure if authority is the best word for it, but what I mean is: You come across as more of an authority, more likely to be accepted as the real deal, if your book is published by a big name publisher or a publisher who is respected in your field, whether it is animal behavior or literary fiction.
Second, publishing with an established publisher, particularly for a first book, is a great way to learn the ropes. What is good copy editing and how cruel does it need to be? What is stacking? What's a galley proof and what can you do with it? So, doing your first book with a big publisher is actually a good fit. You get the credibility and you learn a bunch of stuff that will come in handy if you decide to self-publish later.
Notice I said "good reasons to publish 'a' book with a major publisher." You might find that one is enough with a big publisher. Or you may decide you just want to go ahead and get on with putting out a book.