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Only three words put E first and N third. There is no strategy here, just three entries and the reason there are so few.
ENNUI is the one word on this page most people would recognise. It means a weary boredom, and it is also the one entry here that repeats a letter.
ERNES and ETNAS are the other two. An erne is a sea eagle and an etna is a heating vessel, so neither is vocabulary you would produce during a puzzle.
E is a common opening letter but almost nothing in English puts an N in the third box behind it at five letters. Each of the three uses a different second letter, so there is not even a branch to describe.
S closes two of the three, which is the only distribution worth stating. If your puzzle has an E first and an N third confirmed, read all three and pick the one that fits.
Yes, by a wide margin. ERNES and ETNAS are valid but neither turns up in ordinary writing.
No. ENTER has N in the second box and T in the third, so it sits on the E first and T third pattern instead.
A sea eagle, usually the white tailed eagle. ERNES is the plural and it is the five letter form that lands on this pattern.