Generally speaking, it depends on what the manufacturer specializes in. Shops that do milling or lathe work will be able to take STEP or IGS files at a minimum, and may also be able to take other native CAD files depending on what they happen to use in house (Solidworks, Inventor, Fusion, etc.). Shops that mostly do 2D work like plasma/laser/water jet cutting will probably want dxf/dwg because that's what their software uses. 3D models usually won't help them because the production process doesn't make use of 3D models like milling or turning does.
For quoting purposes it's customary to only send a dimensioned 2D drawing first. The reason for this is that the 2D drawing will usually have extra information in it that the model doesn't. This would be things like material, dimensional tolerances, any kind of special finishing or other processing, etc.. For more complex parts it's common to put a note on the drawing saying that the 3D model will be provided upon quote approval. This way the shop can take that into account when determining production cost.
Whether or not the shop actually will use the model depends a lot on the complexity and what type of part it is. Milled parts with 3D contours pretty much require the 3D model (STEP, IGS, etc.). Simple 2D flat parts that don't have a million holes can many times be done right off a dimensioned 2D drawing, although sometimes the model is handy of there are a lot of holes or weird shapes. If in doubt, you can always ask them and they will tell you what they need/prefer.
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