Just speaking from my perspective, this is how it can work in the USA with several possibilities (maybe much more than you want!!):
1. Military( IN A NUTSHELL! I CAN GO INTO MUCH MORE). Once you get a degree from an accredited University (preferably an engineering/technical/quantitative curriculum) you enter into the USAF/USN/USMC/Army/Coast Guard. Upon successful completion of respective flight school, you are sent to a replacement air group (RAG) for specific training on the airframe you will eventually fly. The process from 2NDLT/ENS to Fully trained, winged aviator takes about 3 years. In a 8-10 year period, most aviators who choose to leave for the airlines have served as Aircraft Commander, Section Leader, etc. Most have well over 1,000 hours. Many have graduated WTI, Fighter Weapons, etc. It is my observation that most military aviators (depending on the circumstances) with good records are hired by the majors straigh up. A few will choose other airlines depending on their circumstances. Although it varies, my observation is that many of my friends, hired by majors served as 737/MD-80/DC-9 FOs, and then either transitioned to jumbos within a few years or stayed for about 6 years or so in their airframe and became Captains. Others went out and bought their own type ratings (most on 737s) and were hired by others. Some bought FE certificates and moved on to cargo companies. There is no set way, but by and large the military is the best route to go, IMHO. I did it, serve as a reservist, and got to fly the F-4/F-18--won't trade that for anything.
2. Ab-initio. This is the most popular way right now, due to the hiring flux. You go to a school like Comair Academy. They will teach you how to fly. You get a degree. Once you get your private/me/ifr, you stay on as a flight instructor to build up your hours. Once you have enough you go on to a guaranteed interview with Comair or another airline and get on as an FO. Two years as an FO and you become Captain of an RJ/Brasilia/SF-340, etc. From there you apply to the majors. All told--about 12 years before you make the big bucks, but this is an effective way to do it.
I guess a lot depends on the conditions of the market, the airline you are applying to, etc. Most American pilots have spent a long time in the military or building up their hours with commuters/air taxis/small cargo (you need about 1,500 hours (500 as PIC of turbine/me) just to get a look).
The airline's needs, your domocile, and seniority will determine the aircraft you fly. You won't see many young, inexperienced 23 year old 767 FOs flying between NY and London. Most have paid their dues.