Hi Sara,
As far as "disciplines" go, we tend to categorize our sources by nationality, though admittedly this becomes inaccurate and anachronistic when you look closely enough. Hence you will hear people talking about the "Germans," the "Italians," the "Bolognese," the "English," etc. If you can, I strongly recommend getting a copy of Joachim Meyer's "Art of Combat" translated by Jeffrey Forgeng; ISBN: 978-1848327788. It should run about $30 or so. He covers multiple weapons, such as longsword, rappier/sidesword, dagger, dussack, pole weapons, and unarmed combat, all done unarmored. He's German, and based his book on the German "system" of Johannes Liechtenauer. Other good places to start are Ringeck, who deals with Liechtenauer again, Paulus Hector Mair, and a manuscript many people refer to as the "Doebringer manuscript" (MS 3227a), all of which should have translations to work from on the Wiktenauer site.
The Germans are the ones we have the most sources available as far as quantity, and also the ones for which we have the most English translations. The Italians, I admit I am less familiar with, except for a couple of rapier sources. For the English sources, we have very few surviving ones, apart from George Silver and Joseph Swetnam. Both are very good to read, though Silver is much more theoretical and opinionated. Both also require a little effort to get past the archaic English.
If you're interested in rapier, (another light straight pointy sword) though, I would recommend Giganti as a good one to start with, and also Fabris and Capo Ferro. Giganti is available as "Venetian Rapier" here:
http://www.freelanceacademypress.com/ and Capo Ferro is titled, " The Art and Practice of Fencing." Fabris is apparently and unfortunately hard to come by. When printed in modern editions, our sources tend to have limited and small print runs, so get them while you can.

Ultimately, you can start wherever you want, but I find the above sources to be good starting places, plus, of course, getting assistance from more experienced practitioners.
David Kite
ARMA in IN