Do I use a relay, MOSFET, or just a switch? (5VDC 15A load)
You can use a simple p-channel MOSFET as a high-side switch.



simulate this circuit &ndash; Schematic created using CircuitLab
The particular part listed above is cheap and has an Rds(on) of less than 2.5m\$\Omega\$ @25°C with 5V drive, so it will drop less than 38mV at 15A, so it will dissipate about 0.8W when hot, requiring a few square cm of copper to run reasonably cool. A slightly more expensive part (still less than $1.50) is more like 2m\$\Omega\$ @25°C so it will run cooler.