I'll second Mike's rec of Mach 3. I would not go with Mach 4. Not yet anyway.
Budget is going to be a big factor in your solution for generating the g-code (aka toolpaths) to run your new machine. Creating the code for the 4th axis isn't too bad as long as you are only dealing with 3 of your 4 axes. You just convert one from inches (or mm) to degrees to get the rotation (this is probably the simplest part of the whole process). If you want to actually work with 4 axes, that's multiple orders of magnitude more complicated (and expensive). Everything below assumes 3 axes total with one being rotary.
Cheapest - get a free spreadsheet program with a macro language and use your superior math and coding skills to generate the toolpaths. This will keep your mind sharp for sure, but it gets old fast.
More Expensive (roll your own option) - Buy a cad program to generate your design "flat" (in two dimensions) and buy a cam / wrapping program to generate your toolpath and convert it for rotary.
An integrated CAD/CAM package is about the same price as the roll your own - Buy something like Vectric's VCarve Pro (~$600). It has limited ability to generate wrapped output but it should be able to do it. Or you can get a cheap wrapper program to convert a "flat" toolpath to rotary.
Much more expensive - Something like Vectric's Aspire ($2,000). You get full 3D modelling tools and the ability to see your wrapped design. It's not perfect. The wrapped features are not as fully developed as they could be because their customer base in more oriented to the flat world. But you can do a lot with it, it you work at it.
Insanely expensive - There are some really nice programs for jewelry designers out there. The companies will be happy to let you use them for about $10,000 / year (last time I checked). That wasn't in my fun budget, but the software looked really nice.
If you are just starting out, I would suggest getting comfortable running flat work for a while before you start trying to do rotary work. There are a lot of basics you need to get sorted out for yourself before you start complicating things with rotary work.
Vectric is a great company with a very active / helpful user base. Their online forum is a great resource. They have free trial versions of their software to help you understand what you would be getting into.
Ed