What ships SHOULD they have used in the Dominion War? The answer is obvious: every ship.
The real question is, What wartime ships should have been constructed?
First, do you already have warships in construction? Increase production of these. Next, do you already have plans to begin construction of warships? Accelerate production of these.
Second, do you already have multipurpose but combat capable ships in construction? Repurpose these to warships and accelerate construction of these.
Now this is where it gets a bit more complicated, and it depends on the empire’s focus. Is it short or long-termed? In other words, you want your empire to win the war, and—and this is the important part—to be well-situated after the war.
That means construction of multipurpose ships should not cease entirely but should remain at least slightly higher in proportion to your competitors combined. This will give your empire the best possible chance to win the war and best possible situation after the war.
So, for the Federtion, for example, it would mean constructing a number of warships, such as Defiant class, repurposing a number of multipurpose starships, such as Excelsior class, and constructing a limited number of new multipurpose starships, such as the Intrepid class. Meanwhile, all ships would be put to the war except a handful of those reserved to generate a good situation post war.