However, it is still better to balance what people near you want, with what you want. If you are not choosey what you want, aim for what the "buyer" wants. If you want a oarticular kind (heck, I wanted to breed PK, but it was not going to happen since it voted 1, while halfmoon and crowntail got more than 8, and doubletail got over 5...)
My PETCO sells giants, but I fear that even if I established a good line with them, people would still be turned off because they came from "petstore fish".
Also, what defines a giant? I have been seeing listings on AB for "GIANTS", but they have long fins and look like normal bettas?
No, the fins have nothing to do with it. There can be veil, plakat, etc for giants hence longer or shorter fins.
You want to start with pet store fish, it's your choice. Not ours. If you get a line going (breeding A1 back to parent), it would not be so bad. Just know it will be harder and the results will be wacky the first few times before the line is established.
The "giants" in stores are generally half giants. you will get normal, or slightly larger fish from them. A true giant should be about 2.5-4 inches in body alone.
A giant is just the size of the body- theoretically they can come in any fin type but PK, hmpk, and hm are the most common by far. The only issue with breeding a petco giant is finding the right girl (they don't sell giant females), and IME petco giants often don't have great colors.