Since you're riding many different horses I would go with something that has a changeable gullet, like Wintec, Bates, or Collegiate, or something with a flex tree like Courbette's Swiss line of saddles. Wintec is a (quality) synthetic saddle, the rest are good quality leather saddles. If you don't want to hassle with changing the gullet plates every time you ride a different horse, then I'd go with the flex tree saddle.
Courbette's web site: http://www.courbette.com/Catalog/catalog.html
The first section of Swiss made saddles are all made on their flex e-motion tree. I have a couple of friends with these saddle and they are very nice quality. The regular size flex tree fits most horses medium-narrow to medium-wide. The Magic saddle is made of all-weather leather, which is nice if you trail ride a lot.
The other direction you could go is a used Stubben Siegfried in a 30 or 30.5 cm tree. This tree size fits most horses quite well (except the big guys). Even the 31 cm tree fits a lot of horses. You'd just need to use a thick pad for a more narrow horse. Stubbens are GREAT saddles and worth their weight in gold. You can find a nice used one in the $250-600 price range, depending on how good of condition it's in.
The seat size is for you. I would recommend a 17 to 17.5" seat. Try to find a retailer that has a trial policy, so you can test ride a saddle to make sure it's comfortable and the quality you want. For your height and weight, a 16" or 16.5" would likely be too small. You want to be able to fit 4 fingers between your rear and the end of the saddle, and 3-4 fingers between your pelvis and the front of the saddle (at the same time). My mom is 5'5" and 120 lbs and a 17" saddle fit her just right. My daughter is 5'1" and 110 lbs and her 17" is only a tad too big for her, but she's still growing!
Good luck saddle shopping!