Mid-to-late afternoon and Monticello are your deciders here. If you get in any time between 3 and 6, it will take you just as long to get to Quantico from IAD or DCA as it would from RIC, but from RIC you'll at least be moving. I don't think slawecki's road signage concerns are really that big a deal; north out of RIC on VA 156 (the exit everyone uses) past I-64 to I-295 north to I-95, then the reverse coming back.

If you know you'll do Monticello, as a local I would suggest putting CHO in the mix on similar terms as RIC. It's 20 minutes farther from Quantico, but the extreme simplicity of CHO (6 gates, rental cars right outside the terminal door, right-right-left and you're on US 29 north) vs. RIC (more tangled access than an airport that size really merits) is worth it.