A whole lot of action on this site as of late with a bunch of action on the threads so I figured I'd kick in some advice from the quiver that has worked for many a pilot, including myself in the past.
GET A JP FLEET GUIDE. For those in the cheap seats, get a bloody JP Fleet Guide.
The JP Fleet Guide is a book that plane spotters use as porn for pilots, but it's also a perfect start for the budding aviator with 'round about 1000 to 2000 hours (or less frankly).
Decide where you want to start looking as far as the area of the world and start hunting. The guide has the types flown, fleet numbers and contact details for literally every air operator on the planet with aircraft bigger than a C182. Then, send off the CV's and call as many as you can. After that, if there are some bites from operators in a couple of places that you think you might want to spend some time go buy yourself an around the world ticket. Due to the current 'crisis' you can get around the world one way, with the odd side trip and 4 or five stops, for around a couple grand.
I have a close personal friend who took this exact advice, with a total of 320 hours and a multi IFR, and went to a small African country about four years ago. C206, C208, ATR42 and now a B737NG (the company paid for the rating and he was paid during training, just like it should be) he's in HKG having a ball.
A quick note for those with a bit of turbine time, Solenta out of SA does a bunch of flying all over Africa and the ME. There are a few nice little TP operations out of the Emirates. PNG (the country)always seams to require pilots. The Hawaiian contracts for Dash 8's in Japan are quite good money wise. India is very good money for TP guy's; better than many Jet jobs.
I think the days of young aviators whining about the QOL in Alaska flying a B1900 are over for a while guy's. I've seen the odd snippet alluding to that kind of thinking, but it's going fast. The reason I mention this; overseas operators have no time for 500 hour cowboys who watched Top Gun a few too many times, and there are no laws keeping them from throwing your but out of the company and country at whim. I saw a guy's (bad)reputation follow him from the Gulf to Canada once so try to keep the old nose clean as the contract world is unbelievably small.
Be cool and a bit humble and you will do well. If your serious about it then good luck. Worst case you don't like it and go back home to flip burgers. Best case is you have a blast, some wicked experiences, meet some very cool people and end up in the left seat of a jet making good money in way less time then it would have taken you back home.
Just my two cents, again. Hope it helps.