I don't think this will be very easy to do, the way you want to do it.
As was mentioned, raster to vector programs will probably not give you usable results. I've periodically looked at different ones over the last 10 years, and haven't seen one that I'd use. Of course anyone selling a raster to vector program will tell you how great their's is. They'll all convert your image to a vector file, and even the free ones will do it pretty well. The key, though, is that these conversions aren't very good when it comes to using them for cutting parts. When you zoom in closely to look at them, they are composed of LOTS of short segments, very jagged, and going in all different directions. A simple curve that could be drawn in a CAD program with a single arc, might consist of 100 segments in a raster to vector conversion. This is important, because when you create g-code form your .dxf file, the tool will follow the vectors exactly as they appear in the .dxf.
As for your other questions.
MasterCAM is about $10K, and is far more than you'll ever need. A very good package for woodworkers is Vectric's V-Carve Pro. It's a very capable CAM program, does very good raster to vector conversion, V carved lettering and also has some basic drawing and vector editing. Support is second to none as well.
You'll also need a control program like mach3, which is what actually runs the machine.
Computer specs are not cumulative, however, if you want to use one PC for both CAD/CAM and machine control, be advised that while the machine is running, you really shouldn't be using the PC for anything else. Separate PC's is a good idea.
Tracing in CAD. What that means, is load the image into the CAD program, and manually draw right over it in your CAD program. The CAD program will have commands for lines, arcs, curves, and other entities. You use these to draw your shape, using the image as a guide.
I'd recommend that you start downloading demo and trial software and try to do what you want, and see if it's feasible. Feel free to ask a lot of questions along the way, because the learning curve may be steep.
I don't think you'll be able to get clean, tight joints on your inlays with your method. Ideally, you'd draw the whole thing in a CAD or design program and skip the raster to vector step. But that will require you to get good at a CAD or design program.
In the meantime, I think you'll get better results by hand tracing in CAD, or hand tracing over your raster to vector conversion (to clean it up). Then, I'd print out scale drawings to use as templates to cut your veneer to, so that you can get as close a fit as possible.