If pheasants are on the list, then go for the 28 over the .410
And if weight is an issue, avoid Mossberg, Baikal, etc.
The CZ bobwhite/partridge/ringneck etc are on scaled frames and very light, and I think the Savage 555 is as well as the Yildiz
decide if you prefer SxS or O/U then go from there.
With some searching you will be able to find a decent gun, though closer to $1K rather than $500. Ammo really isn't as hard to find any more, but if scarce in your area just buy lots when you do find it. It doesn't go bad.
The 28 Gauge is my favourite and I have several shotguns in 28. Oddly enough, the one I use the most is the least pretty of the bunch: the CZ partridge