Engine is too weak to compete against a Duchy/Duke strategy. The question is how to go for it. Squire, Beggar and Trader are all really nice for putting together a deck that can hit $5.
IMO, I'd open Trader/Beggar. I think overall Beggar is a better choice and Squire. Getting either 3 Copper the turn you play it or 3 delayed Silvers next reshuffle (Trader in hand) is just much better than +$1 and 1 Silver next shuffle. Because in a Duchy/Duke slog the extra Copper is not bad. With 3 Copper you just need a single Silver to hit $5. Support from Trader should provide enough. Beggar + Silver (or 2 Copper) is also $5. I'd continue to buy Beggars at $2 and $3 getting 3-4 of them. I'd probably get a 2nd Trader after the opening turns and then buy Beggar if money is $2-$4 alternating a few Silvers in there if you just aren't connecting Beggar and Trader or if you haven't hit Trader with Estate/Trader. Get Duchy at $5 every time you can. Library is not worth it. Win the Duchy split and then switch to Dukes.
Edit. I agree with what SCSN says. Trader/Beggar into Silvers will be too slow and mass Beggar will work fine.
