So just make the decision: either spend $125 (pretty affordable) for a sharp and sexy new dovetail saw or spend $50-$200 on a vintage dovetail saw that will require sharpening and likely rust removal. I typically advocate buying antique woodworking hand tools, but in the case of back saws I prefer new Lie-Nielsen saws. I don’t currently see the progressive pitch saws on Lie-Nielsen’s website, but you can always call them and ask them to file one like that for you. But the normal dovetail saw will work great.
Sound overwhelming? Then just start off focusing on Disston saws. The Disston saws were manufactured by the millions and are the easiest to find, and most are of exceptional quality, especially the below common models. Remember to buy pre 1940’s era vintage hand saws. Here are some ebay searches for wood saws. To ensure that you don’t over-pay, when you’re on ebay click “sold” to see what they’re selling before and to see which saws are desirable. It’s fun research: