Here is a, not so simple, answer.
A little history of the FE is in order. Many many years ago, circa 1930s, airliners had Captain, Co-pilot, Flight Engineer, Radio Operator, and Navigator positions for the longer range international type flying. With advances in technology the Radio Operator and Navigator positions were combined into the other three leaving us with the Captain, Co-pilot, and FE. At that time the FE was not a pilot position. It wasn't until the mid 1950s that ALPA started advocating that the FE also be pilot qualified. This, along with other manning issues, led to a rift between ALPA and the pilots of American Airlines. With American Airlines eventually separating from ALPA in 1963. The early jets; B707, DC-8, B727 all had FE positions. It wasn't until the 737 and BAC 111s that the 2 man cockpits were introduced in jet aircraft. All larger international type aircraft such as the 747, DC-10, and L-1011, even though newer generation, still had the FE position. It wasn't until the 757/767 came out in the early 80s that a large jet was built without an FE position. Most airlines still had a majority of aircraft with the FE position.
A pilot looking at going to a major airline back in the 70s and 80s needed to have the FE written completed. It was very rare to go to a major airline and not start out as an FE. In fact, when I was first looking into a career in the airlines in the mid 80s it was considered pretty good if you only had to be an FE for 5 years before upgrading to First Officer.
No two airlines are the same in regards to career progression and it is constantly changing. What we can say today for Fedex, American, United, etc will be vastly different in ten years time. If you truly want to fly international then Fedex and UPS would be good choices. United, American, Delta, Continental, Northwest, and a few others would also be good. Right now Fedex and UPS would be the two top airlines to have a career at as their pay and benefits packages are superior to all the rest. United, Delta, and Northwest are in bankruptcy.
International flying may sound glamorous and fun, but it is very fatigueing and shortens your life. At some airlines you may be lucky to stay landing current averaging only 1 landing per month. For those reasons you may want to choose an airline that has a little of both. That way you can go do international for a few years to get it out of your system and then move back to domestic which is so much easier on the body.
TP