1. The tank itself. Some fish, even bettas, are kept in tanks. Perhaps by themselves or with others. If the tank is filthy, the other fish are sick, dying, or dead, or the fish you want is sick or dying, the fish obviously won't be healthy.
2. Signs of sickness or stress: Ich, velvet, columnaris, discoloration, burns, cuts, missing scales, clamped fins, dropsy, pale coloration, popeye, etc. You'll know! :)
3. Behavior. Those who do not react to movement, color, or even tapping or touching the glass/cup, are stressed and/or sick.
4. Flaring: Sometimes this is good! It shows the betta's reaction is very good. However flaring can be from stress as well.
5. Fins: rot, bite marks, and tears. Over flaring, sickness, bad water, other fish and stress!
I try getting fish the day of shipment
I know it's every other Thursday the fish come in. This way you can also see if the other new fish are ill, and if they are like baby bettas who were probably together, one who has columnaris gives the others a chance of having it too. Choose wisely! Adult VS baby? Adult. Babies are cute, but lots of work!