I guess my #1 concern with that is ruining them! I've never used a lathe, but I think my local community center has a wood shop I can convince them to let me use. If I could find someone to make them for me, I might do that, but I can't seem to find anyone.
Cocobolo @ Rockler is $25 for a 3x3x12 blank... does that sound about right? http://www.rockler.com/product.cfm?page=19219&filter=cocobolo
This Mora is really beautiful: http://www.rockler.com/product.cfm?page=22663&rrt=1
I'd suggest getting a piece of maple along with a piece of cocobolo. Use the maple as a test run and use the cocobolo (or what ever more expensive wood you choose as the final product). The lathe isn't really a difficult machine to operate, but it takes practice to turn good work.
You should check out a few youtube tutorials before you start since you've never turned before.
HaydenHD on youtube is my favorite to watch, he turns a lot of interesting things that you can translate to grado cups.
Just remember to keep the design of your cups VERY simple to start, and remember to measure very carefully. If I were you I'd look for a blank thats 4x4x2, that way you have some extra material to hog off since your a novice. I usually make my cups about 3-4 in in diameter (depending on the type of cup) so 4in should give you at least an inch to work with.
Lastly, when working with Hardwoods, make sure the chisels are very sharp. If possible, have one of the people at your local shop sharpen each of the chisels that you're going to use. Which reminds me, make sure to view tutorials on which chisels you need to use and how to properly use them. To get you started, I generally use: a bowl gouge, a scew chisel, a roughing gouge, a parting tool, a spindle gouge, and a custom tool made by EasyWood Tools.
There's a million more things that you'll need to know before starting but hopefully you'll watch/read some tutorials before you start Turning on the Lathe.
Good Luck, and I hope it works out for you as Turning can be really fun.