Hi Triton,
Actually, I kind of suspected that I saw the handiwork of Eddie Floyd in there, but for some reason I can't find any links to his work anymore.
For practice thrusting, let me recommend hay bales as a good beginning medium. They're cheap, and have enough substance to them to show you when your thrust is offline. They also last a very long time as long as you don't hit the twine too often.
Cutting with a rapier is one of those questions that will get you different answers from different people.
Remember, there are a lot of people who insist that period rapiers weren't even sharpened except for a few inches near the tip. I personally disagree with this theory if for no other reason than soldiers through out history have typically disliked dull weapons. It may have started out dull, but I suspect the blades soon acquired a fairly keen edge. (Given the limits of the blade geometry.)
Given a sharp edge, some cutting is possible, but of course it's never going to be anything like what a nice XVIIIb will give you.
The trick to it is a "Draw cut." The idea being to hack into your opponent, then draw the blade through the flesh deepening the cut the same way you'd cut a steak. Obviously this would be one fluid movement and when employed against limbs would be very effective in doing what the FMA guys refer to as "Defanging the Snake."
Otherwise, the non-thrusting cuts were limited to "tip cuts" which would be something along the lines of the previously mentioned "Stromatzione."
The "Stramatzione" is a quick flicking cut using only the foible (first few inches) and usually aimed at the eyes or just above the eyes, the idea being to blind your opponent. Whether you got the eyes themselves or merely inflicted a head wound that would bleed into the eyes, Some level of the desired effect was acheived. There were even specially designed rapier blades with a rather bulbous leaf shaped point that was intended to provide extra cutting power to the technique.
Obviously the tip cutting principle would be very distracting when struck anywhere on the face, and such cuts to the neck could conceivably be lethal or at the very least, extremely un-nerving to the recipient.
These type of blows were often used in duels which were not "To The Death" but "To First Blood" and one desired only to "pink" his opponent rather than inflict serious injury or death.
Either way, the only reasonable hope of a rapid kill was by means of the thrust, and this was how the period Masters taught. Weaken or disable with cuts, kill with the thrust.
I personally prefer Swept Hilts and "Shell" type hilts. This includes Pappenheimers and your particular sword as well. There are a lot of reasons for this and none of them mean that cup hilts are "bad" in any way.
Cup hilts are a bit too late in history for my chosen period of study. (Specifically about 1550 to 1634 A.D.) They did not appear on the scene until (earliest known specimens) about 1640 or so. So when you see those Movie Musketeers sporting Cup hilt rapiers, realize that it is an anachronism akin to seeing a Colt 1873 Peacemaker .45 in a U.S.Civil War* movie. (The character D'Artagnan began his travels with the Musketeers in 1625.)
I have fairly large hands and I find that many cup hilts are a bit too cramped and don't allow the flexibility of grip that is required for true versatility with the rapier.
This, almost above anything else needs to be stressed about the rapier. Your grip on the sword is a <b>very</b> fluid thing. You must be able to roll, tilt, slide and otherwise move the grip around in hand to be able to properly realize the potential of the sword.
The Pommel is also very important to proper technique. When holding the blade at extention, the hand should be relaxed with fingers lightly curled, but not squeezing the grip. (Think "cradle") The pommel should rest against the bottom of your forearm. To understand the reason for this, think of your wrist as a fulcrum. By simply "popping" your wrist down as you flick your fingers upward, you get a surprisingly fast movement in the tip of the blade. This is where much of the rapier's speed comes from. Speed comes from the fingers and wrist. Power comes from the shoulder and elbow.
BTW, from a historic point of view the Disney "Three Musketeers (Sheen, Sutherland etc.) was horrible. The 1970's MGM production with Michael York and company was incredibly well researched and executed.
*Correctly known as "The War of Northern Aggression." After all, I'm an Arkansasan!
) call it something else?