For the majors, you need some recency and probably 1000 turbine, ideally 121 but 135/91 might do the trick in the right aircraft.

If you do a 18-24 months at a regional you should be able to get hired by LCC/second tier such as Spirit, Jetblue, Alaska, etc maybe even SWA. Or you could stay, upgrade, and get some TPIC and shoot for the top-tier which includes FDX/UPS. Worth applying to any top-tier you'd be willing to work at as soon as you meet their mins, but you're probably going to need 1000 TPIC to get called.

With some turbine time, you'll have some options (unlike in the past). So you should start educating yourself about the various airlines, domiciles, contract/pay, culture, fleet, etc. All else equal, always pick airbus over 737.