I won't discuss the fancy armor shown in the TV series because reasons.
But since you have added the books tag and you are okay with it, here goes.
It is simply unknown as of now.
Others, as an intelligent distinct species, are completely shrouded in mystery. Little to nothing is known about them, their origins, their customs or their way of life. They are not like their minions, who use the same armor they were wearing at time of their death. The armor they don is no ordinary armor. Every inch of it screams out "MAGIC".
"Had many talks with George. He told me of the ice swords, and the
reflective, camouflaging armor that picks up the images of the things
around it like a clear, still pond. He spoke a lot about what they
were not, but what they were was harder to put into words."
-Tommy Patterson (Comic book artist for the series)
A shadow emerged from the dark of the wood. It stood in front of
Royce. Tall, it was, and gaunt and hard as old bones, with flesh pale
as milk. Its armor seemed to change color as it moved; here it was
white as new-fallen snow, there black as shadow, everywhere dappled
with the deep grey-green of the trees. The patterns ran like
moonlight on water with every step it took.
So that proves that their armor is not of human craftsmanship.
Let's take all of the possibilities that you have listed and discuss them one by one.
Do they make their own in an industrial fashion?
Plausible but extremely unlikely. Others are not known to do that kind of manual labor nor does the Wild North offer such resources to be used as Raw material. Because if that was the case, Wildling realm would have developed craftsmanship on par with the realm South of the wall. But then again, they could be using magic, as you suggested but the key thing to remember about magic in WOIAF is that it's not Harry Potter magic where you just whip out your wand and do it. Every bit of magic requires certain raw objects to work (Such as Dany's sacrifices to give birth to her dragons, Kingsblood concept etc). What exactly would the Others have to make their brand of magic work?
Did they steal them?
Steal them from whom? The Night's Watch? The Watch doesn't wear the armor like the others do. Nor do any other humans. There's no one else to steal from.
Are they hand-me-downs from another age?
We do not know. They could have some sort of arsenal intact somewhere in the North, long forgotten since the Battle for Dawn, as were the people who probably built it.
What family? We do not know if the Others even have a concept of family or heirlooms or if they could even procreate to build a family.
GRRM is silent on the matter as far as I know. He will probably use his standard response "Keep Reading!" if asked, I am afraid.
In my humble opinion, it may be that it is some sort of magic which requires certain sacrifices to build super weapons (Craster's children giving power to the weapons like Nisa Nisa did to Azor Ahai's sword?). In any case, the canon answer is:
We do not know.
Disappointing but that's what we have so far.
UPDATE: As Skooba kindly pointed out, GRRM has hinted that the Others make their own swords. When asked about their swords:
Ice. But not like regular old ice. The Others can do things with ice
that we can't imagine and make substances of it.