Choosing a tribe is something you do at character creation, so often it's not kind of a big deal. You choose your tribe and it's kind of part of your character concept.
But you do want to go another way. That's perfectly fine. It's part genetics, part tribe politics and part tribe totem's will.
Let me elaborate:
a) If you have someone with "pure blood" as background, he will look like a hero of old of a specific tribe. A pure blooded Fury will look like an amazon from the days of Ulisses or Troy. A pure blooded Fang will have beautiful golden hair and will look like some hero of old tales.
But why does this help you? Has your character pure blood or any of his ancestors? Gotcha. That might be a ticket to the tribe you wish for.
(The Fangs have a tight grip on their kinfolk to keep the Blood pure.)
b) Tribe politics. This is kind of a no brainer: No humanborn Red Talon, no male Black Fury and so on. So if your character has some characteristics that can be ticked of a list of no-gos, he cannot get into that particular tribe.
c) The will of the totem spirit. You see, there is a reason why the Furies do not have male Garou within the tribe (except the metis ones): Pegasus told them to (why now doesn't matter). So a male cannot be accepted because Pegasus told them to.
So as you see for choosing the tribe there are (at least) three things that are to be considered. So can you choose your tribe ingame at your own leisure? Yes and No. I haven't found any rule as written, but you get the gist once you familiarize yourself with the tribes.
My take would be the following:
- Fangs - unless you have purest of pure blood you won't be able to get
a foot in that one.
- Furies - don't be a (non-metis) male, and then you can be a Fury.
- Bone Gnawers - don't be an arrogant prick and poor.
- Children of Gaia - I think they take everyone, but not everyone wants
to be part of them.
- Fianna - well that one's tricky. I'd guess that if you have a heart
of passion and can drink way more than ony other of them you could be
part of them. (Helps to be on good terms with Stag, but well that
helps with every other tribe as well.)
- Fenris - show your battle prowess, perhaps best one or two of them in a fair fight (and get Fenris himself on your side).
- Glasswalker - show that you're way better with the computer, gadgets or machines than one of their other cubs and they might consider. (And since they - like the Bone Gnawers - don't have pure blood that might be your only chance (if you don't know your ancestors))
- Red Talons - don't be born as anything other than lupus
- Stargazers - if you can keep up with their constant philosophical musings and like to live your life in austerity, they'll welcome you with open arms.
Shadow Lords, Uktena and Wendigo are tribes where I'm at a loss, since I don't know them that well.
Tl;dr: Get the tribes totem spirit on your side and impress the tribe with your will to join them and excel in their virtues and they'll welcome you.