As far as pumps go, I really like the Winchester 1200, especially over the far more popular 870. You can pick up a 1200 for around $150.
Semiautos will be hard to bring to a lot of countries, but the best in my opinion is the Remington 1100. Low recoil, classic looks, and a ton of them available used. In fact, it is much better to buy a used one preferably pre-1980s as they have become crap as of late. For something more reliable or durable, the Beretta 391 or Benelli Montefeltro are great choices. The Montefeltro is extremely light which is something that cannot be said for the 1100 or 391. I have used the 391 and the Montefeltro on dove hunts in Argentina and they can stand up to 1000s of shells a day with no problem and minimal cleaning. In 20 gauge, they are also extremely low recoil.
For a real international hunting shotgun, you are probably limited to an O/U or SxS. I have had O/U shotguns in varying price points from the Stoeger Condor that I got for $300 to the Winchester 101 at around $1500 to Beretta Silver Pigeons at over 3k. The Silver Pigeons are great guns and have definitely earned their reputation but for me that stand out was the Winchester. Still, I have never liked O/U guns and rarely use them. I am much more of a SxS guy. My personal favorite is also an old classic, the Fox Model B. I like it more for sentimental value than anything else as it is not a great gun, but it is reliable and is probably over 60 years old at this point but still flawless. You can probably pick one up for under $300.
If you want an actually great SxS, you cannot do better than AyA without getting a London best. I am preferential to the No. 1 deluxe RA but that is only because I love fancy round action sidelocks and it is truly an heirloom gun. You can get an absolutely amazing No. 2 or No. 4 for a fraction of the price if engraving and fit and finish are not your highest priorities. The fit and finish on the 2 and 4 are amazing but not quite 1 deluxe level. As you can tell, I really like round action game guns, but I do also have a thing for box locks like the Fox and the No. 4 is a perfect example of one.
