I designed the chassis in Solidworks so it's easy to export the front and the back faces with all the holes to dxf/dwg format. From there, what would be the best way to go? I basically need the labels and some kind of numbering around the controls. What software do you recommend for this job? ...
What's needed depends on the requirements of the shop which will produce the plates, and how much you're willing to pay.
When I bought non-standard faceplates, I used a trophy shop near me. Their website & FAQ specified what artwork they required (and how much I'd be charged if I had them do the artwork from scratch). They accepted .jpg, .bmp, .pdf, .gif and many other types (but then charged to convert them into a vector format). Among them was the Corel Draw file type, and others here mentioned they'd used a free download version of Corel Draw to do their faceplates. Fortunately Corel Draw is a vector file, and saved me the Art Charge on my order.
Custom plates are gonna be expensive, for a setup fee if nothing else. After the one-time setup fee is charged, you can generally have additional same-plates made fairly inexpensively.
Whether any one shop is cheaper than another is really up to you to find out. Call/visit websites, ask the shop you're thinking of using exactly what they have available, and what their requirements/fees are.