"Claycrusher1900," if I were in search of a hammer-gun within the price range you suggest, my focus would be on branded guns from makers or retailers W & C Scott, Army & Navy, and Charles Daly. You will probably locate more damascus-barreled guns than those affixed with steel sets, but there is nothing wrong with that attractively patterned barrel material or limiting when combined with their usual 2.5-inch (the elder 2-5/8 inch chambered gun will work too) chambers. I shoot the 2.5-inch cartridge (and in 2-5/8 inch chambers) more than the 2-3/4 inch cartridge, even in guns originally chambered for the longer cartridge. Beware of guns that have had their chambers lengthened; personally, I summarily reject them. The short cartridge, which was and is still to-day chambered in a number of bore sizes, is available commercially and in a wide selection of loadings that match most needs.
Have careful measurements (or request them to be) taken of barrel wall thicknesses and also look carefully for dents or for signs of them having been raised, and for riveling along barrel surfaces, examine the barrel set as well for loose ribs and rust and for its remotest indication, and consider the quality and extent of repair work, if any, and determine if it has been too excessive or extensive for safety concerns more than for the consideration of aesthetics. A famous gun-writer once wrote when asked about the three most important aspects to be inspected when considering a double-barreled gun on offer. I paraphrase his informed response: "the barrels, the barrels, and the barrels."
By the way, because 10-bore guns were not employed as much as the smaller bores of their heyday or thereafter, these larger bore guns are usually in better condition than their contemporaries, and their chambers can be reduced and re-chambered anew to accept the 12-bore (2-1/2 inch, 2-3/4 inch, etcetera) cartridge by chamber sleeves, if the gun is reasonably light enough (and not a rarity or highly valued collectible) to make it a sensible conversion.
I would further recommend that you buy the English-made gun here rather than overseas. It will be less expensive and more convenient to buy domestically, especially if you are careful about from what auction or retail company, or from whomever, you make your purchase. You will find your Daly gun here, of course.
If you are not comfortable making your purchase without expert advice, or perhaps feel you are not familiar enough with hammer-guns or a particular one to take a decision, you might consider consulting a gunsmith or gun-maker in the States who is known to be expert, or alternatively expert as a purchasing / condition review agent on behalf of a potential purchaser, and also one that will help you for a reasonable dollar amount.
I have personally purchased excellent though carefully chosen exemplars of the aforementioned makes over the years and have not only greatly enjoyed pride of ownership, but also the indefinable excitement of putting them to purposeful use afield, and to the challenge at the range; so I feel quite confident in commending them for your consideration. And surely, the romance of owning and using a fine hammer-gun to good purpose is not to be discounted.
Good luck with your search and final selection. Please post photographs of your ultimate choice.
Regards,
Edwardian