When looking to purchase a fish, what signs do you look for to make sure they are healthy and won't die as soon as you get them home, or infect other fish in your tank?
personally I look at the fishes color, fin quality "make sure that there aren't any missing or torn" and how active they are in the tank compared to the other fish.
Don't buy any fish from a tank in which there is at least one other fish appearing sick - if it's sick, there is a good chance it might have infected the others, although the symptoms may not yet be visible on other fish. Many diseases begin to show a while after you purchased the fish. Other than that, the fish should have good coloration (as opposed to being pale), they should swim in a well-balanced manner (as opposed to erratic swimming and scratching against objects, or darting motions), their fins should be erect and stretched out (as opposed to being clamped), and of course there should be no spots of any kind or films of any kind on the fish's body. The fish should also have a good appetite.
I usually ask how long the lfs has had them( I never buy just received fish), ask if they are on a centralized system( meaning all tanks are connected) If there is a fish sick in any tank I don't buy that day. then I just observe the fish I want. How is its color? how does it act? bullied or bullying? just a few of the things I do.