The last two projects i have done have both been blasted using a glass bead media back to bare metal.
The glass bead media leaves a surface that does not require a lot of rubbing down before a priming coat is applied.
If I were you I would have the engine bay and underside blasted, this removes all the unwanted debris and leaves the areas fresh for refinishing, in my opinion a freshly refinished engine bay does lift the project to another level.
Again the underside can be finished with whatever medium you prefer before being overcoated with your choice of topcoat, once more in my opinion lifting the whole appearence.
My last vehicle was cleaned top and bottom and a few more extra bits, all done in one day from leaving to returning to the workshop, this particular project had been sprayed underneath with some sort of stonechip which would have been a nightmare to remove other than by blasting.
It cost in the region of £500 but money well spent in my opinion.
Of coarse its a case of "horses for coarses" you can sand down using your DA cheaper but the blasting gets into all the places the DA cannot.