I don't have myself a 3D printer yet, but i have been messing around with 123D by Autodesk. Its free, you can design items to you exact dimensions. Here is a link http://www.123dapp.com/design
I would check out this link http://www.reprap.org/wiki/Useful_Software_Packages. Ive used most on the list and would say they all have Pros and cons so its whatever you feel comfortable modeling in use. Autodesk 123D design can be a little flakey at times but overall a good Digital modeling software.
A number of classes I give to young learners involve free design tools like TinkerCAD, which operates entirely in the browser and has an easy interface for exporting 3D model designs. You can do much more work with meshes designs in Blender, which is another free package usually used for animation work, or using simple tools like the 123D Suite by Autodesk who also makes the MeshMixer product for combining multiple 3D models before printing them. Nate's link is one of the best places to start - take a look at NetFabb for fixing holes, etc. The basics you can get from TinkerCAD without any cost or software installation.
I would like to see what happens with TinkerCAD with the recent purchase by Autodesk. LIke you said, it is a very easy tool to use. I also liked it ran in the browser.
