Where do I connect the LED light strips to within the fuse box?

Connect both sets of lights to the same junction point in the fuse box. Don't make extra work for yourself by doing it twice. Black wire is always ground. You will need to remove a screw or nut under the dash that is a metal ground point.(usually near the fuse box is one with a bunch of wires fastened to it) Crimp on a U or round connector to the black wires from the lights. Fasten the new connector with the other wires to ground. The red wires need to be connected to the fuse box. I would use the radio fuse for this. They make a metal clip that allows you to pull the fuse, hook the clip to the fuse, reinstall the fuse and it will give you a tab to slide a crimped female spade connector to it. So a trip to Radio shack, or any hardware store will help with getting the connectors unless you already have them

If you wanted to put in a inline switch this would be the time to do it. Then you can turn the lights on and off when you wanted to while the car was on.