Right on! So first off lets determine the difference between a zip line and a speedline. A zip line has no control on the piece of wood or tree being removed. A speedline is set up with some sort of control line on the piece being sent down the line.
I would recommend DMM Revolver carabiners or small pulleys for attaching to your speed line. Carabiners work fine but I find that the added friction makes it more difficult to get pieces moving quickly.
Webbing loops are great slings. Buying 1" tubular webbing in bulk is a great way to save money. Use something like a Beer Knot to make an endless loop. Girth hitch this to a biner and then girth hitch that to the limb you want to zing down the rope.
I tend to like a method I call "freeballing" the zip line. This is when the ground anchor is not a stationary object rather it is a ground guy holding the rope. This method is quick for lighter pieces but if the piece were too large could cause the ground guy to get dragged across the ground, the piece to drop and damage anything underneath, or for the grounds man to be dragged into the uncontrolled piece. Use at your own risk.
Usually the ground anchor is secured with a port-a-wrap or with a 3:1 then to a port-a-wrap. This helps to tension the line and to reduce the drop in the line. One thing to keep in mind is vectors on your rope when speedlining or ziplining. Vectors are the direction of force, in this case, on a rope. The more tension placed on the anchors, in tree and at the ground, the higher your vector force will register along the rope. As a piece of wood is loaded and sliding along the speedline it creates forces far greater than those associated with normal pulling of a rope.
This is illustrated very well with a simple example. After you are done climbing and have descended out of the tree walk until you are at the end of your climb line. I'm assuming you will have quite a bit of rope and a very good rope angle from your tie in point. Now, lean backwards into your harness and your rope until you are almost laying down. Have your grounds person pull on your rope trying to pick you up. More than likely you won't move very far. Now have your grounds person reach up as high as they can on your rope and pull directly down. Even the lightest of workers should be able to easily pick up the heaviest of climbers. This is possible because of vectors and multiplied force. The downward pull on the rope creates huge amounts of force with barely any effort.
This plays into the fact that your speedline could be anchored into the removal tree or adjacent tree. Be sure that if the pieces to be removed are large that the anchor is large as well along with the entirety of the trees structure.
Aside from all the math and physics, speedlining is badass and can take a ton of work out of your job. Send pieces down a rope directly to the chipper. Awesome!
Here is a ziplining video from a couple years ago that I made. Pretty sure its my first GoPro video.