Petco and PetSmart could in theory have good fish departments. Central filtration properly run has UV sterilizers and the can bring the possibility of disease spreading from tank to tank to very minimal, assuming they are maintained. The Petcos in our area all run the marineland systems, where each 4 foot three level section is a separate entity. PetSmart, really I've been into one and paid attention to it though, has me shaking my head and I walk in and see a beautiful system and few fish and the ones that are there don't do well.
They need to have good people, and with the way the fish hobby is going that might be harder to do than it was 30 years ago. They need to just flat out stay away from some types of fish unless they're going to make the effort to house them right and learn about them. Unfortunately, I'm not sure that they look for fish expertise, they just look for some retail savvy if possible then "train" their employees to where they sometimes aren't absolutely horrible at fish (I used to be an assistant mgr at a Petco, after owning a fish store for 7-8 years before getting into other lines of work)... it's a common problem with a lot of corporate retailers. We actually have a guy at the Petco in our town I'll buy from and a guy in the next town I'll buy from that actually knows his stuff pretty well, other than that I'm going to the very few lfs all over the region to buy fish from.
On the goldfish, I can pretty much guarantee that any new aquariast with a 10 gallon that picks up 15 20 feeders will fish the majority of them out in 4-8 days. 3 to 4 at least have a chance. I'd have to look at Petco's and PetSmart's feeder tanks before I'll pass judgement on how their feeders will do. They can be amazingly tough. I used to own an aquarium shop and had the typical problems with feeders. I thought it was nuts when one of my suppliers said to try something, it worked great... would have been another story if the filter hadn't been established though. I went weeks at a time without losing feeders after that. A bare 40 breeder with a well established Emperor 400 on it that you do a 100% WC with straight cold tap water about an hour before the fish arrive can do wonders with feeders if you throw stress coat and about a cup of rock salt in it and just float the feeders to equalize temp then pour off all of the shipment water elsewhere. I had about a 2 year run where my goldies were flat out not dying even though the same fish were dying elsewhere. We used to bring in 1-2K a week. One time my supplier said he wasn't going to be by for 3 and I needed to order heavy and I brought in 4K, I might have lost a handful out of that batch.
I just recently got back into the hobby. Started my tank with 6 platies, then 3 weeks later it was 8 rasborah hets, 8 rummynose, 3 catfish and two ottos.... more than I wanted to do but it all worked. A much bigger tank than the OP has, and I bought a piece of anubias on driftwood that I put in the directed outflow of the filter that no doubt helped establish the tank. Tanks can be started with fish, but one has to be careful.