Both your first choices are great and well regarded. I’d say the Hamilton is more “field watch” aka outdoorsy, general wear, and the Orient is dressier aka office, but also general wear.
I’d actually suggest starting at a different point (especially as there are “many” Hamilton Khaki models and “many” Orient Bambinos. Go to a store, and try a few on, note the size and features (and perhaps commonality) of the ones you like. Then based on that, look around a bit more.
Using the Google will also let you find lists of best watches at certain price points, and looking at sale listings will give you a sense of what is available and general pricing on the used market. There is something nice about buying one new, though, and given the season, you may stumble into a decent deal.
Hamilton and Orient are great brands for your price range. Take a look at Tissot, Certina, Glycine, Mido, and a few others as well. Good luck, enjoy the search, don’t feel rushed.
Realistically, no one has ever noticed a watch I’m wearing or worried if it’s dressy or not 😁
Try the bracelet and if you find it comfortable, then it’s worth getting. But comfort and your taste rule.