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N first and I third covers 18 words, and only three letters ever sit in the box between them.
A takes about fifty percent, O thirty three and E seventeen. No other letter appears there at all.
NAILS, NAIVE, NAIRA and NAIAD sit on the A branch, and NOISE and NOISY on the O branch.
NOISE and NOISY differ in the last box, which makes them the quickest pair to settle once an O lands.
NEIGH is the only E branch word anyone would name, so an E in the box between is close to an answer on its own.
NOISE is the strongest opener, since it is the most common entry and its S and E cover endings the A branch also uses.
If it misses on the O alone, NAILS and NAIVE are the two to work through next.
No. NIGHT puts I in the second box and G in the third. The I needs to sit one place later.
They share their first three letters and split across the last two, so a guess on either narrows the A branch by half.
It names a water nymph and it is the least familiar of the A branch entries, so it is the one to save for last.