My question is, is bismuth bronze good enough if I somehow arm my dwarves properly, or should I try to get iron one way or another?
Lucky you, I can only arm my militia in copper for now.
Bronze will be good enough for generic troops, yes, as Nil noted. However, you will struggle as further waves of ambushes and sieges come.
Sieges only hit at 80 dwarves, so you'll have a good couple of years (typically around year four for me) to gather steel from humans (melt down everything iron and steel that they bring!) and dwarves to begin arming up your army.
Also consider investing in a bit of crossbow training - bones are ubiquitous, for one reason or another, in every single fort - and bone bolts make for cheap (if relatively weak) ammunition. However, a goblin that looks something like a porcupine will still suffer, even if the bolts are as weak as nerf darts.
I also know where the magma and adamantine is thanks to one particular save that I have backed up, but it would require me to dig down over 100 z-levels just to use it and I'm more of a fan of smaller, compact fortresses. I usually get my first invasion after two or three years at most, and by then I am nowhere near ready half the time since I suck at training my dwarves. So now I actually have another question.
I have tried numerous times to train my dwarves, but it takes forever for them just to get the skills I would like for them to have, because normally I have to rely on immigrants just to get any sort of weapon or combat skills. Usually by the time I get invaders the melee units are about halfway ready to being able to fight off the invaders, while the ranged units are nowhere near completion since half the time I don't have someone who can make crossbows and the other half of the time I don't have bones.
What should I do in particular to better manage my military in regards to it's training and it's arsenal? Any weapons that I should focus on crafting by the way? I tend to like spears for some reason, as I read that they can do critical damage pretty easily correct me if I'm wrong. Should I go for something else?