[G&K] New to the game, and trying a science victory!

Hi there, this'll be my first post on the forums and definitely not my last :)
I bought Civ 5 along with the Gods and Kings expansion pack a few days ago and am loving the game, but am finding it quite hard. This is the first game like this I've EVER played, this is the first strategy game I've ever layed eyes on, and am happy to say that I love it.

I really want to aim for a science victory to be my first victory in a game, I've read up on some Civs to go for, and am thinking of going with Babylon, as the early GS, I feel, is amazing. That being said, I know little about the game.

I'm just asking, what type of tech routes should I take? Should I start at Pottery and go to Writing for the fast GS? Or start with something like Animal Husbandry, or Mining? Just wondering if there is a specific route I should take when playing Babylon.

Secondly, I'm wondering what I should start off with as my first production, I've started with monument every time I've played to get a fast settler in the Liberty tree.

Also, when should I start expanding? And go to my second, third, fourth city etc. Basically, I just really want to know what route I should take, because right now, I feel I'm just making random choices :lol: On my first Science Victory attempt I lost out to Ethiopia because they somehow won on the Utopia Project, and had a huge army.

Thanks in advance, and thanks for taking the time to read this!