I always though Kirk's Farragut
-class; according to the Star Trek Chronology
he was posted there in 2254 - nine years after the original launch of Enterprise.
Perhaps the SS Conestoga
was based on the design of the SS Valiant
, launched 4-5 years before and a proven spaceframe - a logical idea given that at the time (2069) building starships was a relatively untried and expensive business with limited expertise.
Food for thought: perhaps the USS Valiant
was the same class of vessel as our new friend the USS Kelvin?