I need to know the word type of "before" in constructions like the following:
Before going home, I had a beer.
I do know the word types before can be in general, so no need for lengthy responses ;).
This really depends on the principles of your particular analysis. Two broad approaches:
Which is more appropriate depends to some extent on the purpose of your analysis.
The first approach has the benefit of consistency. In this approach, we say that prepositions can take complements, just like other elements such as verbs. And we say that prepositions can be intransitive or transitive, just like verbs and quantifiers. That complement can then in fact be a 'verb phrase inside a noun phrase' (gerund in English, but potentially something else e.g. a verb phrase with a subjunctive, in other languages), just like subjects and complements of verbs. Or in other words, the category of the head word doesn't change according to its complement or transitivity. This makes sense if you consider how we treat verbs: in "he drank" vs "he drank alcohol", we wouldn't usually say that the verb changes into another base category just because it is used intransitively. Similarly, in "they regretted the decision" vs "they regretted deciding so early", we wouldn't usually say that "regretted" changes category. So there's little reason to do so for prepositions if you want to be consistent.
On the other hand, you might decide that you do want to encode features of complements in the base category that you assign to a word if it suits your application. So you might want to have an extra category, e.g. called "conjunction", to mean what is effectively a preposition that takes a verbal complement.
For what it's worth, traditional Victorian grammar would generally take the second approach. Though not for any particularly compelling reason.
But it's really up to you: what suits your purposes best?
In your example, before is used as a subordinating conjunction.