(Background that you can mostly ignore if you'd like)
So I'm trying to replace the bottom bracket on a new bike that I'm building, but I need a bit of help. The main idea is this: I have a GMC Denali (which runs fine-ish) that I disassembled as I prepared to clean and repaint it, but recently got my hands on an older, lighter Fuji frame. So I decided I'd just transplant as many of the parts as I could from the Denali to this new frameset.
(The actual conundrum)
One problem I'm running into is that the Fuji doesn't have a bottom bracket, and I'm not quite sure on the specific of what I should get to replace it to use the crank arms from the Denali that I already have, and I don't know the model of this frame because I can't trace the serial to anything online (and I think part of the serial is worn away). What I do know: A usable replacement for the Denali measures 68mm BSA and 122.5mm, aaccording to the fellow that posted this video here.
So I'm pretty lost as to what I should do. Should I buy a new bracket? If so, how do I identify what taper I need, what length I need, what other parts I need, etc? Can I transplant the original bottom bracket? That will require a 20 dollar tool that I'd have to purchase off Amazon, because of ring attachments that hold the BB in, and if so, can I just buy a new bracket and install it for cheaper than buying that tool?
If anyone can guide me through the general process of what to look for when replacing a BB (how is it done? Does it depend solely on the crank set used, or the frame as well? Is the BB shell size usually standard? etc.)
I'm very much a newbie here, and googling has basically yielded "take it to your bike shop so they can fit the right BB." Any help would be appreciated.