I am no expert, so just my thoughts...
I think you meant 68-122.5. Those bb-un300s have a collar on them that I asked about in another thread, so wondering how that limits crank choices (I honestly don’t get the collar).
As far as shifting 3 x 7, you could get nice 7 speed shifters and use the current Tourney stuff before diving into new derailleurs. But if you want “new”, XTR stuff is top notch during that era. Deore XT as well and they won’t cost that much. Crankset as well.
As far as I know, all 7 speed Shimano is spaced the same so you have lots of options.
Some questions to ask
Is the FD bottom pull or top pull?
Are the rings in good shape?
Is the gearing presently good for your needs?
Would better tires be a better investment?
Are brake pads good?
As far as tools, just the crank puller and bottom bracket tool. Be sure to secure BB tool to remove/fasten. Those can slip off. Maybe the BB is good!
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