Hey, I just started reading the Divine Comedy last week. Here are my thoughts.
One, don't just read Inferno. You're cutting out two thirds of the work.
Two, after every canto, I read summaries/commentaries from wikipedia, and sparknotes.
I've been using the text/translation from the Princeton Dante project, which includes some more commentary.
Having read at least the Aeneid helps a lot. Virgil is a big part, so being familiar with his work is important.
After every few cantos, I've been listening to this guy's lectures: http://oyc.yale.edu/italian-language-and-literature/ital-310 . This might be overkill depending on your level of interest, but I find it fascinating.
I'm no expert, just a STEMfag trying to culture myself. Additional background info and commentary has been invaluable, even for just figuring out what is going on. For example, everyone likes to talk about Paolo and Francesca in Canto V, but the name Paolo is never even mentioned. If not for commentary actually explaining the story that they were adulterous lovers who got murdered, I wouldn't have understood what was happening at all.