Military straight to mainline
I'm a Reserve baby (i.e. was hired off the street into the Reserves, not prior active duty), and I built my hours by horing myself out to my squad ("troughing"), then flew a couple years with Atlas. I think having some 121 time on your resume helps & lets you check another box.
With that said, I've had numerous squad mates get hired with no 121 experience...one guy which was in the first Delta new hire class.
I wouldn't jump to the regionals or ACMI carriers until you've built some PIC time in your squad. Just my opinion.