I think the question really ought to be whether you want the gainer at all. If you want the gainer at all, you probably want it first, since if you wait for a few copies to come off the stack, then the pile is close to empty, and when are you really getting the advantage anyway? What is the reasoning behind wanting a card, wanting to get some of that card, and THEN wanting to pick up a card whose purpose is to gain more copies of that card you've already started in on? (I'm genuinely curious, and there probably is a situation for it, I'm just not really seeing it right now).
As for whether or not you want to go for the gainer or go straight in for the "key card", that depends on a number of things. The rough gist of it is that you need to figure out whether you want to get the key card AFAP (as fast as possible), or whether you want as many as possible. Of course, sometimes both will be true, but usually it slides one way or the other as to whether it's more critical to get a "critical mass" or to get started. The trade-off you usually make is that you're down one 'key card' for a shuffle, then you're even the next shuffle, and it's only the shuffle after that in which you get ahead.
Interestingly, I think Junkers are one of the clearer cases, but in the opposite way of what you've said: You almost never want to get a gainer for a junker, but rather go for the junker straightaway. The point here is that you are trying to win a split, but it's not the junker split - it's the junk card split (e.g. curses). And because the junk hurting their deck is such a big deal, making the shuffles bigger and the decks worse earlier on seems like it's almost always going to be more important, than getting a bigger split. It's also important that junkers aren't really cards that you just want lots of, really. The exception would be cultist, because of the Lab clause, but the problem there is that there are so few gainers - University is clearly too slow, whereas Altar is actually an interesting question, but of course there are good chances you draw it dead, terminal collision, etc. which usually make you just heads-down rush the cultists.
When you're talking draw engines, because those components you gain speed up how fast the shuffles go, it's often not worth going for the gainer at all. And this is usually when you go for delayed gainers - not in order to get a "key" card, but to improve consistency later in the game, where you are buying more expensive things and gaining out components to maintain your engine running.
In general, there aren't many cards you want to open gainer for, but the ones that exist are usually incremental advantage cards: cantrips with some little bonus, that don't help you draw that much.
As for the specific case of FG, the gainer regains the tempo on turns 3/4, and if you hit on turn 5 exactly as first player, you can win the split - IF you are contested. If you aren't contested, then the gainer is almost always going to get you to your 10 faster, or if you're lightly contested, it will help you win the split more. Keep in mind that you need the thing to actually give you an extra gain of an FG: Workshop is probably high enough chance to do so (though depending on what else you have to workshop after FG are gone, possibly dubious anyway), even though you could potentially hit Estate-Estate-Estate-Copper-Workshop, but Hamlet on turn 1/2 is probably a bit too much of a risk.
In general, gainers get helped a lot by having more than one target card to grab. An Ironworks won't help me win the Caravan split by much, and I'll behind until nearly the time they run out. But if there are both Caravans and then Advisors or Caravan Guards or even Vagrants, then the Ironworks gets a lot better.