I'm planning to install baseboard and carpet in my basement. I was wondering if I should install the baseboard first or the carpet? If installing the baseboard how much of a gap is needed off the floor? I was told 1/4" or 3/8"?

Baseboards go in first and then your tackless striping stands about 1/2" out from the baseboard. When the carpet is install use a stretcher to get the carpet attached to the tackless. When you remove the excess use cutter made to slide along the wall and then drive the edge of the carpet down into that 1/2" space between the strip and the wall.

Base board should be 1/2" off the sub floor 1/4" would not be enough to tuck the carpet, and as ballenger stated for everything else.

You'll probably need to paint/repaint the baseboard after the carpet is installed. The kneebanger thing can chip the paint.

Repainting the baseboard is always something that might need to be done. The kicker should never make any contact with the baseboard if you know how to use it. The stiff edge of the carpet can act like a scaper and the cutter can leave marks so I'd agree.