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Whether you manually trace a raster image or auto-trace using Inkscape's Trace Bitmap, or some other trace engine, depends on the complexity of the image, and your own personal preference. Also perhaps the quality of the raster image would be a factor. (For example, I saw someone once using designs for a cutting project, like from a kit or something, which had been photocopied so many times, it was nearly impossible to get a good auto-trace.)
Auto-tracing almost always injects some tiny bit of distortion, here and there. So if absolute precision is needed, that would point to manually tracing it, where you can make it as perfect as you want.
Plus, auto-trace does not produce a single path. From what I understand, if your project is etching something into the material, but not cutting all the way through it, auto tracing gives exactly the kind of results you need. But if you're planning to cut some part of the material so that it's completely separated from the original piece, then you need a single cutting path. And auto-tracing gives you 2 paths. So even using auto-trace, a good deal of editing is usually needed (for cutting as opposed to etching).
PDF is a file format which can contain both raster and vector contents. Inkscape will be able to edit the vector contents, but not the raster. Raster contents will need to be either manually or auto traced. BMP is a raster format, and so would need to be traced one way or the other.
I can't think of any reason to manipulate a raster image in a raster editor, before importing into Inkscape. Not unless there might be a way to improve the quality of the image, so that auto-tracing would be more successful. But I'm not very familiar with raster editing, so others might have more helpful comments about this question.
If you run into specific problems, please feel free to share your SVG file and give us all the relevant info. If the question is about Trace Bitmap, please include the imported raster image in the SVG file.
I've had a couple of tutorials in mind, since I've learned how to make videos. One of them is how to use the Pen/Bezier tool. (Actually the whole community needs to have different tutorials for each tool -- I mean for the Inkscape website. But that's another story.) I don't know if I'll get it done in time to help you, though.
From what I understand, often you can buy vector files, for cutting or other use. It seems they usually come in some vector format besides SVG, for some reason. But they can still be used in Inkscape. Well, there are probably free files available too, but for cutting projects, probably not so much.
