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One hundred one words put C first and A third. Three consonant clusters take most of them, but the branch you actually want is the smallest one.
H takes the second box in thirty seven words, thirty seven percent. L follows on twenty seven and R on twenty three. Those three together hold eighty seven of the one hundred one, so CH, CL and CR is very nearly the whole pattern.
CHAIN, CHAIR, CHALK, CHARM and CHASE come from the H branch. CLAIM, CLAMP and CLASH come from L. CRASH and CRAFT come from R.
The trouble is depth. CHARD, CHARE, CHARY, CHARK, CHARM, CHARR, CHARS and CHART all share their first four letters, so landing on that stem narrows almost nothing.
O takes the second box in only ten words, ten percent of the pattern, and yet that small branch holds COAST, COACH, COALS and COATS. If your puzzle allows an O in the second box, check those before working through the clusters.
They differ only in the last box, so as a pair they are wasteful. Take one and spend the other turn outside the H branch entirely.
Twenty eight, which is twenty eight percent. E follows on seventeen and T on twelve.
CHAR is a real word on its own and English hangs a lot of endings off it. That inflates the count without adding any variety to guess against.