Do you mean what qualities did they look for when sacrificing, or what they were looking for when 'reading the entrails'?

Qualities picked when sacrificing basically meant picking the best looking animal; good colour of hide, blemish free etc. Goddesses would often get female animals, Gods tended to get male animals. There's a hierarchy of animals too. So sacrificing a big oxen gets you loads of brownie points with the heavens; sacrificing dogs not so much (though it still went on)

Reading omens from sacrificed animals 'reading the entrails' / Haruspex is pretty shady. It's like asking 'what do you look for when reading tea leaves?'. But they'd commonly inspect the liver. I think some records indicate that priests may have had liver charts to compare it to. Other times they just used their divine skill, as it were, to come up with a reading.