These days, I use Kilz Premium waterborne primer. I usually go over that with high end "latex" house paint. If I need to fill a hole, I use whatever outdoor rated filler I have at the time. I don't offer a glass smooth finish on HDU, so the Kilz Premium & house paint work great for me. Technically, HDU doesn't need primer, but I've always primed it.
Most of my HDU signs are from a single piece of HDU and have a routed background, which gives them raised letters & decorations. For mountable individual HDU letters, I route them upside down, and machine holes for mounting studs. I have a vinyl cutter/plotter, so I use the same hole pattern to plot the hole locations for a drill pattern.
I have screwed through the face of HDU to mount, and just painted the screw heads the same color as what they're screwed through. They've been far enough away from view that the customer didn't wasn't to pay to have it blind mounted, or to have face screws hidden.
Aspire 9.5 - FlexiEXPERT 11 - Vytek Rebel 4' x 8' - 5HP Perske Spindle