Hmm, well, look for American made saddles that retail (REALLY retail) for $1,000 or more if you want to stick with good quality (like Ammerman). Older (1980s or older) Circle Y, Textan, Billy Cook, Big Horn, and Simco saddles are good. Newer ones are not so good... Cactus saddles are amazing, but hard to find (small shop). Colorado Saddlery saddles are decent. Courts saddles are very nice as are Crates and Henderson.
Southern Trails sadles are nice for the price, and reasonable.
Western Saddles, Trail Saddles, Barrel Saddle, Ranch Saddle
Trail saddles will work, "All Around" saddles will work, a rough out training saddle would be fine too (though pommel and cantle are low, not a lot of security), "buckaroo" saddles would be fine, as would a wade or ranch saddle. True roping saddles will be quite heavy, so that's something to consider.