For me, level has no real bearing on what I buy. I prefer to buy animals that have a decent coloration/pattern breeding prospect and show a good bill of health with as few red stats as possible. Truth be told I don't usually look out for green stats so much as a lack of red.

I prefer nameless animals so I can name them, but it's not a breaker for me if they're already named. Gender is a bit of a tossup - I prefer females but a good stud is always a worthy investment.

As far as researched genetics goes, I'm actually kind of ambivalent. The price point of a researched prospect animal is usually more than what I would typically pay for. And the gamble of an unresearched animal, provided it has a lack of red modifiers, is something I kind of enjoy.

I prefer to buy wild caught, unused pets. Researched genes is not a requirement but a little bit shown does help, especially for caught pets. I don't care about names and I am primarily after pets with rare recessive genes. I'll consider anything with red stats if they are the strong 50% or 30% decreases because it means the pet may carry a gene with a lesser genetic power than the red. However I will check the parents' genes.

The 25% green stats generally don't interest me unless they are in addition to any rare recessives or the stat is something I require for a specific purpose (like agile paws for counterstrike).