When choosing a minhag (custom) or halachic opinion, you might think there are two choices: Ashkenazi or Sephardi. That's not quite accurate. Ashkenazi and Sephardi are geographic categories, but they are not inclusive of every group. There are many "ethnic" groups within Judaism: Mizrachi, Ethiopian, Yeminite, B'nei Menashe, Kurdish, Lithuanian, Chassidic groups (in some communities this may be akin to an ethnic grouping that shows a geographic origin), etc. Each group can have its own minhag or halachic ruling. Because of this, the "Ashkenazi" community may have several options for you to choose, even if you are choosing to actively associate yourself with Ashkenazi tradition.
As a general rule, you are an Ashkenazi or Sephardi based on the community you live in when you convert. If you are single (and especially if you're a single female), you can change your "affiliation" upon marriage to someone with an established family heritage. Only if you want to, of course - though some will tell you that you don't have a choice. (Though marriage has a way of mixing customs around even for those of the same heritage - every family is different because of this.)
But most converts are not completely Ashkenazi or Sephardi. Because of the unsupervised nature of most converts' Jewish education, we pick up customs and rulings from everywhere. In fact, we're given the halachic freedom to choose the minhag we want, though we may be required to take the halachic rulings of our current community (which is not a given nowadays).
In effect, no matter which kind of community you learn with and convert with, you probably have a mishmash of traditions. And you know what? That's ok. Embrace that freedom rather than seeing it as a weakness. Arguably, few Jews today have a "cohesive" tradition because of changing tides within the community at large. Baal teshuvahs pick up a mishmash of traditions too (and sometimes even have the same latitude of choice as a convert), then they have kids who carry on those mashup traditions. Members of communities often consider "their Rav" someone who is not the leader of their community (often a Rosh Yeshiva from a yeshiva or seminary), so few communities have a cohesive community tradition. There are a lot of Ashkenazi/Sephardi marriages today, which creates kids with a cornucopia of traditions. Converts are not the only one with Jewish traditions equivalent to a Girl Talk mashup song (some NSFW language).
But really, what are you? Because people will ask, and you'll need to come up with an answer. I personally call myself "Ashkenazi by Default." What do you say?