Alexandrian and Seax Traditions are both descended from the Gardnerian Tradition. Alexandrian incorporates some Judeo-Christian ideas, along with Greek, Egyptian, and Celtic ones. Seax Wicca uses aspects of English Saxon and Scottish witchcraft. I believe these both are also initiation only.
Dianic Wicca is a lot different, instead of there being both a God and Goddess, there is just the Goddess, and she is both the male and female halves of deity.
There are also Family Traditions, which are passed on through family members, so you can't really study those unless you've got family who is already a part of that.
Now, my personal favorite, is Eclectic Wicca! That means you can get ideas and use aspects of whatever you want, so long as you have an understanding of it first. It's both hard and easy to be an Eclectic, easy because you can use whatever you want, hard because you have to learn about all the different things you wish to use.
Those aren't all the paths you can choose from, but they're some of the more popular ones. If there's a specific one you're wondering about, ask me and I'll tell you what I know about it!
In addition to the traditions, you can either be solitary or part of a coven. I'm a solitary eclectic Wiccan, so I work by myself and I use things from a variety of sources. Just because you're a solitary doesn't mean you are forbidden from working with other people, though. I have a close friend I like to work with, and you can go to open circles and whatnot, or even partake in online rituals! Your path can change, too. Just because you start out as a Gardnerian in a coven that doesn't mean you can't change your mind later and become a solitary Dianic or whatever you want to be. It's all about finding a path that works for you!
Also, don't forget, Wicca, Witchcraft, and Pagan are all different things. You'll see we say this a lot, haha. Wicca is a Pagan religion, Witchcraft is a practice that can be a part of Wicca and can also be separate, and Pagan is a term for non-Christian religions. You can be Pagan without being Wiccan.
Followers, if you feel there is anything I need to add to this, let me know!