You cannot bore a hole in a joist within 2" of the outer edges of the width and it cannot exceed 1/3 of the width of a joist. So a 2x6 joist being 5 1/2" wide would allow for a 1 1/2" hole exactly in the middle of the width. You can also notch the edge of a joist, but only in the outer 1/3 of the span and not deeper than 25% of the width of the joist. I'd say you probably can run your cable for option #2.
For some reason multiwire branch circuits are popular on SMC despite their shortcomings (cost and electrical hazards). Price out 12/3 and 10/3 and you'll find they are made of gold. Then compound the fact that you have multiple types and sizes of wire to run. What you really want to do is use a common size such as 12/2 everywhere than you can so that you can buy it in a large spool. Compare the price of 100' of 12/2 to 250' of 12/2 and you'll see what I mean. In my garage they would be even less practical in that all 120VAC circuits must be GFCI protected. If I ran 12/3 to all my outlets then every single outlet would have to be a GFCI outlet and that gets expensive in a hurry and discourages regular testing of the GFCI capability. Instead my two 120VAC general purpose outlet circuits are from GFCI breakers that cost me $35 each. Time to test GFCI? Walk over to the sub-panel and knock it out. But if you decide to run 12/3 or 10/3 because you feel it has advantages too good to pass up then so be it, it isn't wrong to do so.