Majors do not all require turbine PIC, but they all to my knowledge require 1000 hours of some sort of PIC.
Multi PIC is generally not a requirement, and piston ME PIC will not make meet major airline requirements without turbine time.
First off, do you have 1000 hours PIC (ASEL, AMEL, or a combo)? If not you need to get that FIRST before going to a regional where you might have a long upgrade time.
If you have 1000 hours PIC of some sort, then next on your list would be turbine time...PIC preferred, but SIC is better than no turbine time.
If it comes down to it, majors will hire a guy with a bunch of 121 SIC before they hire a 135 piston ME PIC.