Official Sources say that they actually used Excel, believe it or not.
Yes and no. Well, first, I should point out that the anime isn't based off of a manga, it's based off of a Light Novel. The manga (that I didn't know existed) is also based off of the Light Novel.
But there are technically two orders that you could watch the show in: release order and chronological order. Most people watch in release order- that being the order in which they came out- because other than being what was likely intended by the studio, it's relatively easy to follow since you just need to know when it was released. Chronological order works, too, and won't spoil the release order- well, it does, but the release order does the same to it.
Now if you don't want to start with any specific order and just jump in, you can, sure, but there are specific ones you shouldn't watch straight off. Namely, Monogatari Second Season, Hanamonogatari, and Tsukimonogatari. Any of the others are fair game, really, (though I suspect Owari won't be in the coming episodes).