My first book was "Fighting with the German Longsword." Later on I added "Medieval Swordsmanship, Illustrated Methods and Techniques." This week I finally broke down and bought "English Swordsmanship" but haven't had time to peruse it yet.
"Fighting with the German Longsword" by Christian Tobler is a fantastic primer of the Liechtenauer tradition. Good choice! Honestly, if that's the only book on historical swordsmanship that you ever read, it will give you quite a good overview. It has its gaps, and it has areas where I would do things a little differently, but no book can cover everything.
Unfortunately, Medieval Swordsmanship by John Clements has more myths than truth. I give it credit that it was one of the first books that came out on the subject that treated historical martial arts as an actual martial art, separating it from what we see in entertainment, and at the time that was important. Sadly, it really is just a lot of made up techniques under the guise of "historical research", and has a lot of angry tirades against anyone who is doing things differently. That book (and its companion book called Renaissance Swordsmanship) really makes you wonder if the author has actually ever read any of the various historical sources that he so vehemently says everyone should be using.
I have to confess that I also have English Swordsmanship but haven't had time to read it yet... only I have no excuse, because I've owned it for years and still haven't sat down and read through it.
My interests are in the 15th century Germman and the 16th and 17th century Italian material, so sometimes its hard for me to motivate myself to look outside of my box.
