If you've never used any 3D modelling software before, I'd just go for Blender. It's free, and there are plenty of tutorials out there for it, and the interface isn't half bad (unlike, if you compare GIMP to Photoshop say... :rolleyes).
I use Blender on a Mac (and every other platform incidentally), and I really like it. Your actual rendering options are a bit more limited compared to other packages, but rendering photo-realism isn't really your goal here.
It also depends on what you are trying to make. I will always go through Maya (or any of the above programs) to make sure the measurements are exactly what I'd expect, but for more organic creations I'll use Zbrush as well. It's a fun program to use for sculpting anyway. Meshmixer is also a neat program to help you with 3d printing, though I haven't used it much yet.
I've used Shapeways many times, too. They are easy to use, and the quality is good, but be careful to make sure the materials will work for your project. Some materials might be a bit on the fragile side, unfortunately. Also larger printed pieces can get quite expensive.
There is also 123d design and Tinkercad. Both are form the people behind autocad and have some great reviews. I used sketchup for some of my basic stuff a while back but I've seen a lot of people using 123d design lately.
I'm a Sketchup user, for the simple reason that it does what I need, is free, and has a ton of Ruby plug-ins available to it for free that will allow it to do most everything the others can. It may take some work to get used to its interface if you've used any other program though. Its leaning curve is VERY easy, unlike Blender, IMO. I've found that the programs out there that were originally designed for 3d models that were intended to be rendered out or rigged for animation offer way too many tools and options for the novice not specifically interested in those features. Can it draw what you want, and can it output a file suitable for printing? Those are the only two questions I needed answering when I went looking. All that said, whatever program you chose, Shapeways now offers a model check service that will let you know what parts will or won't work for your chosen material. Typically wall thickness and wire size are two of the biggies.
Teach yourself to model in an organized way, and one that produces "watertight" objects, and your problems with 3D printing will be far less when you get around to it.
I like Tinkercad. It is a free ONLINE program. It is best for using basic shapes to make a product. Granted, the basic shapes like sphere, cylinder and cone are low rez. But I generate higher quality ones in BLENDER (free) and import as STL into Tinkercad. You can also use a 2D to 3D extruding program (like the one from Shapeways) to make objects to import into Tinkercad.
One thing of note if you plan on printing them via shapeways is to pay close attention to the material you want to print with. there are minimum specs your files have to meet in reguards to max size, wall thickness, and such that is listed with each material.
As a Mac User myself I really like 123d design. I use it pretty much exclusively for 3d modeling for printing (although you probably want to grab a free copy of netfab for checking your models for printability). I tried TinkerCad and found it a little limited and I didn't like the fact that all files are stored online. Blender although enormously capable has a IMO a steep learning curve to it.
It does come down to what you want to model though - 123d Design is great for mechanical shapes (i.e. stuff constructed from primaries like cones, cylinders and cubes) for more organic shapes it doesn't work well - you need Blender or Z-Brush.
Thanks for the information, both on programs and specifications! I am going to just start playing around with things, see how I go. This will either be amazing, or an expensive foray into 'yeaaah, I'm not very good at this.'
Also as a side note juliegrrl mentioned netfab. There is a free version of the repair tool that can actually be accessed on the web via Microsoft for free. It works pretty well from my limited experimentation.