The Septuagint (LXX) bears upon a number of questions central to biblical studies and its sub-disciplines. Beyond its significance for textual criticism of the Hebrew Bible, it raises questions about the textual form(s) of biblical traditions during the Second Temple period, the written and oral dynamics by which those traditions were accessed during this period, and, since the LXX would in time become the peculiarly Christian canon of the Hebrew Bible, the relations and distinctions between Judaism and Christianity. Also, the discovery of Hebrew and Aramaic biblical texts at Qumran, some of which reflect Septuagintal readings rather than Masoretic readings (though these latter are found in the majority of biblical texts among the DSS), has raised the question of the extent to which the translators were glossing on their Hebrew exemplars and to what extent they reproduced fairly literally those exemplars in their translations.
Speaking on my own behalf, I am particularly interested in the ways that the LXX sheds light on the reception of Hebrew biblical traditions in the Second Temple period. This is an especially important issue, I think, because this reception of biblical tradition formed the matrix/-ices within which the Jesus movements, as expressions of Second Temple Judaism, developed and spread. In other words, had the Septuagint taken a significantly different shape than that which it did, it is likely that Christianity, too, would have developed differently than it did. As two very brief examples, I note the peculiarly Septuagintal readings quoted in Luke 4.18–19 and Acts 15.16–18. In these two Lukan texts, it is precisely the divergences between the LXX and the Masoretic traditions we presume to be more original than the Greek readings that form the basis of Luke's reading of the texts (from Isaiah and Amos, respectively).
Before you participate in the translation efforts here, I recommend you read the introduction to the LXX, and to the LXX of Genesis, included in the NETS files linked to the Front Page (under Septuagintal resources).