In general the answer is 2-3. In this particular situation, it's likely to be 3, since you need to hit $6, and hamlet+menag can't help you that much in getting there off 2 silvers. You need either silver+4xcopper or 2xsilver+2xcopper. The former has 4 of the same card, making menag an ineffective helper, and the latter is tough with only 2 silvers in your deck. Now, if there were wishing well, which would help get to silver+4xcopper, I might opt to stop at 2 silvers.
That said, in this scenario, I probably would have opened hamlet/silver or even hamlet/hamlet, hoping to parlay the hamlet(s) into a double-hamlet turn to win the hamlet race, which figures to be crucial here.