A couple of observations -
U.S. airlines don't care if you've flown a specific jet type. In the first week of training you get assigned whatever's available. At my company alone they've had almost entire classes go the MD-80, another class go to the 737, another class go to the 767 and another class go to the A320. New hires experience doesn't matter. The odds of having a type rating and actually getting assigned to that a/c as a new hire is very low.
Most U.S. airlines value PIC time over non PIC experience, even in their specific fleet types. And yes, that includes TPIC time. A 5000 hr turboprop pilot, with 2000 hrs of TPIC, will rate higher than a 5000 hr jet pilot with no command experience.
Military training is a plus.
Most don't use helicopter time towards their minimums.
A four year college degree is almost a 100% requirement. There are some who get hired without one. If you're on the low end of TT experience, with no, or low, turbine PIC time, and no college degree, the odds are very small that the Big 3 or Big 4 (AA, DL, UA, SW)(~90% of the U.S. majors) will hire you.
You don't learn much on big jets, you just retain the basics you learned on smaller jets(more landings, more approaches, etc). The flying skills are tough to develop on big jets for the new guys but teaching new SOP's related to long haul ops is fairly easy for a new, but experienced, FO.