As someone who watched the 1st season on TV, where do I start with the books and do they have a proper end to the saga?
Poodlestrike and Mifec gave really good answers, I'm going to add on.
The TV show was my entry to the series, and while it has some stuff I really like, (I loved Harry using a hockey stick and drumstick as his wizard tools,) it... doesn't really have much to do with the books. It adapts one of two stories from the books and has a few characters in common, but also uses some of them wildly differently. (I recall that at one point they implied that Ancient Mai was a dragon in the TV show. In the books it's clear that she's just a powerful wizard.) Apparently they were going to do a straight adaptation of the books and then the studio brought in someone who worked on Charmed and he kind of messed everything up. The good news is, the rights to the series have reverted to the author and the rumor is that they are going to try again, but this time Butcher is going to be more heavily involved to make sure it's more accurate to the books.
Which book should you start on?
Technically, you can start anywhere. The books do tell a larger ongoing story, but the author is mostly pretty good at going back and filling in details from previous books. You one you CANNOT start on is the most recent one, because it's technically part 2 of a story. (Butcher wrote a giant book, the publisher said, "if you do this, we're going to have to sell it for $50 a copy," and they agreed to split the story over two books.)
You can pretty safely skip the first two books. They aren't terribly important and they're kind of bland.
Book one (Storm Front) introduces the world and the characters, and while one or two plot elements show up later in the series, nothing is hugely important.
Book two (Fool Moon) is kind of the same. It introduces more reoccurring characters, but there's nothing you desperately need.
Book three (Grave Peril) is where the action starts. MORE major characters are introduced, but this book kicks off the big ongoing plot of the series. There's a party that takes place in this book that has huge ramifications for the main characters and the world that are still echoing fourteen books later. The bad news is that IMO book 3 is the toughest read. I think Butcher was going through a particularly horny phase in his writing, so book three is pretty sexual in some gross ways.
After that, the series hits it's stride, and while not every book is a winner, the series as a whole is pretty great. You could probably start on book four, which is one of my favorites, and go back through 1-3 if you decide you really like it. It's really up to you.
As Mifec said, it has a proper ending planned. The author has said he has it outlined all the way through the end of the series, but he makes adjustments here or there. The plan was 20 books plus a three book capstone trilogy, but he's had to add a few books in to account for other things that happened, like this most recent story being two books. I don't know what the current count is expected to be, so I'll defer to Mifec's count for 22 + the Big Apocalyptic Trilogy.