The engine completely obliterates any big money approach here, to the point that I'd be stunned if it wouldn't win 100% of the time.
You indeed need lots of actions, but fortunately there's this stack of Wandering Minstrels and the engine player can easily get all 10 of them via both Armory gaining and multi-Bridge turns. The BM player can't deny them as buying WM over Silver slows him down quite a bit while it barely affects the engine (unless the BM player gets a ton of them, but then he's playing with a really incoherent deck that's easily crushed by anything with some focus).
Watchtower-Rats is excellent trashing (gain one extra Rats before only playing them with a WT in hand), it's in some ways superior to Junk Dealer even, as early on the extra card from the trashed Rats plus the cycling it provides does more for you than the one coin, assuming that you have enough Watchtowers.
Armory is an excellent card when there are lots of spammable engine components costing $4 or less. The top-decking is so nice: you can either gain a card you need right now, draw it and play it directly (instead of waiting a shuffle), or you can top-deck a card you are likely to need next turn, thus making the whole building process a lot smoother by enabling you to make your own draws to some extent, even though here Armory's top-decking is less crucial because WT can do it too, so with WT in hand Armory just becomes a Workshop.
Wandering Minstrel's reordering allows for great reliability: you can chose which card to draw next because you need it and/or set-up your next turn. Do you have spare actions and a Watchtower in hand? Give me the bridge! A bunch of bridges but not that many actions? A Wandering Minstrel or two please! No draw? Ah, let's get the Watchtower!
Getting a Jester is decent in an engine mirror, but would be absolutely terrible against a BM player. He has just no cards you want to steal, to the point that if I'd flip a Gold I'd probably even give him another one. So Golds and Silvers help him alot, Coppers are whatever, and you are so rare to Curse him and the few Curses hurt him so little (especially because you also discard one of his green cards) that it's not worth it to waste a terminal slot on, especially not because there's a great alternative that you really want: Bridge.
You'll ultimately win the game via a Bridge mega-turn that buys the last 5-6 Provinces at once, or maybe the last 4 and a whole bunch of Duchies. You really have all the time in the world, as the BM player is slower than a community of aging turtles and has no endgame control whatsoever.
If you are not Marin, I would not recommend to try the engine.
This is the most dangerous sort of nonsense to listen to if you care at all about improving your Dominion game. If you always take the easy way out, if you never try to build an engine that's slightly more difficult to execute than Wharf-Fishing Village, if you never try something completely ridiculous even, afraid that you might horribly fail (which you inevitably will, over and over and over again), you will never ever become like Marin, let alone become much better than he ever was, which is certainly possible: Dominion play is in its infancy.
What holds most players back is not a lack of innate intelligence or talent, but a failure to express their playfulness and curiosity, lazy habits of thought that process boards in terms of obvious stock-strategies in stead of having an eye for each kingdom's particular splendor, lacking any sort of healthy contempt for conventional wisdom, not trusting their own experience more than anything, but at the same time lacking the courage to go completely against it, just to try out something new. And what's perhaps worst of all is saying to yourself things like "I'm no Marin"; it's at that moment, with that exact phrase, that you resign yourself to mediocrity, as you'll soon start building an identity around it, and from that point onward, whenever your playful spirit wakens and graces you with a creative idea, you'll have this voice in your head that laughs at it and has you saying "nah, that's just not me". Most players, in short, simply deprive themselves of the freedom to discover what's possible.