Minion and Loan are the two rare cards that do better without big Treasure like Golds or Platinums. Naturally, they work very well together. Purchase one (or even several) Loans early on; this commits you to a Treasure-free deck, which frankly suits Minion just fine and probably improves it. So long as you aren’t trashing your Coppers too quickly, you should be able to ramp up to Minions to take over money generation before you run out of Coppers. And the fact that you never buy any Treasure means 1) you can single-mindedly commit to Minions; 2) you’ll draw your Minions a lot more often; 3) you never have any tough dilemmas about discarding, since you’ll only be discarding Victory cards.
Of course, you still have Estates in your deck, but that’s not a terrible problem considering all the deck-cycling at your disposal via Loan and Minion. This engine isn’t slowed down much by Victory cards, since you’ll end up discarding your hand frequently anyway.
The fact that Feast is available at $4 is great, since it lets me grab some extra Minions without paying for them. Pawns at $2 would have been even nicer, though Havens are decent.
An old combo, but rereading this and it occurred to me that Minion/Loan has some real problems, in that Loan can slow you to getting to $5, and can often have trouble clearing the last few coppers, if you draw it in them in the same hand as Loan.
A far stronger option, in my experience, is Steward. It helps get to $5, it can trash estates as well as coppers, or it can get to the all important $8. It can even be used to help the reshuffle position with its final draw if you know you have a deck left that is stuffed with provinces and want to have a better chance of drawing Minion from a fresh deck.