If you already play in Open D (DADF#AD), or Open G (DGDGBD) you'll find CGCGCE to be easy to use.

If you rewrite those note names as numbers they are: Open D=151351, Open G=515135, Open C=151513.

The repetition of that 1513 pattern allows you to use the same basic chord shapes and picking patterns in all three tunings, just on different strings. For example, a shape that produces a G chord when played on strings 3-6 in Open D will give you a C chord when played on strings 2-5 in Open G and an F chord when played on strings 1-4 in Open C.

Capoing Open C at the second fret gives you an Open D in which that 1513 pattern sits an octave above where it does in regular Open D. I prefer it for playing traditional D fiddle tunes like "Soldier's Joy" and regular Open D for bluesier stuff.