Typical upgrades right now...
Low-tier turboprop operator: 6-12 months
Jet regional: 2-3 years (occasionally as low as 1 year)
A few regionals are longer, even 10 years on some aircraft. You definately need to research a prospective employer and understand their geography, pay, work rules(MOST IMPORTANT!), expected growth, upgrade, and company culture. Make sure it matches your needs...you are in the very unusual and fortunate position of being able to be somewhat picky. Historically most of us had to take the first job offer we could get. But don't work for Mesa or Gojet...ESPECIALLY gojet.
Getting called by a Major...total crapshoot. It can take anywhere from 18 months as a regional FO to never. The most important factors in order of importance:
1) Military flight experience.
2) Knowing someone on the inside. Actually this is #1 but military guys always know somebody anyway.
3) Having an affirmative action affiliation.
4) Turbine PIC time, 1000+ hours
5) Larger aircraft time (737 or better)
6) 121 time
7) Turbojet Time
8) Glass cockpit time
9) Masters Degree