Err on the thin side of 1/4 inch if you use bits which are ground with a 1/8th inch radius -- the most common shape. These bits will only cover 1/4 inch. with wider strips you'll have a lip at the base of the bead. The cove bit should be a bit more forgiving with thicker strips, but since you have to put both a bead AND a cove on each strip that "margin of error" is imaginary.

I've heard the 1/8 inch radius bits work just fine on 3/16th and even 1/8th inch thick strips.

You may be able to find bead and cove bits with a larger radius. If so, they may be more useful. 3/16th inch radius would work fine for 1/4 inch or thicker strips up to 3/8ths of an inch thick. A bit with a 1/4 inch radius will also work fine, and some like these as they leave you with slightly wider strips ( less wood waste) more flexibility at the seam, and a more durable (less fragile) edge on the cove.

using a thickness planer helps ensure your strips are even along their entire length, and increases consistency between strips. Sometimes the saw is a bit off

PGJ