There are 3 big common green creatures, nessian asp, vulpine goliath, and pheres-band centaurs

So, I have 2 questions:
1: How do they rank? Which is the best and which is the worst, and how much better is one than the others?
2: How highly do you take the best one? Between all 3 of them, it should be easy to get more than enough green fat. Is its power level enough higher than the others that you want to secure that specific fatty over the rest at the cost of another useful card?

I'd say asp wins just barely over goliath by virtue of cost one less (and that one less is colored, too.) Plus it is just as hard to kill. If I was already heavily into green, I might consider the fox over the asp.

Centaurs are not terrible, but I'd choose most green creatures over them, if available, and consider another color depending on how early, what's available, etc. He is a huge blocker, which is nice, and stop most of the biggest guys. He might win out over the others in some cases depending on how many solid threats I already had, but I'd think that would be rare. Alternately, he could work in a combo/control deck better sometimes. But most of the removal he dodges the others dodge as well.

I would think most of these would be outclassed by other more efficient spells in green a lot of the time. Again though, none of them are bad at all, and you'll see them often, so this is a good question.

Does staunch-heart warrior also count as a green fatty?

I would rank them:
1(polukranos, world eater)->
2(arbor colossus)->
3 nessian asp (and nemesis of mortals)->
4(nylea's emissary and centaur battlemaster)->
5staunch-hearted warrior(nylea, god of the hunt and (anthousa, setessan hero)->
6pheres-band centaurs and vulpine goliath

The first 4 groups are the ones that make me want to play green.

Asp is a decent pick 3-4, goliath and centaurs make an OK pick 8-9. I like the centaurs fine since I don't mind paying 5 for a 3/5 in most limited formats, and a 3/7 is just a huge roadblock and wears bestow like a champ.

The asp is pretty solid in my book. 5 for a 4/5 is decent enough, the reach is pretty relevant and the monstrous ability puts it ahead of the other common green fat.

The vulpine goliath is in an odd place for me. The trample is extremely relevant when you start pumping him and 6/5 for 6 is a solid body. For some reason though, I often have a hard time finding space for him. I think it's fairly easy to get some powerful late game creatures in this format, so he's more easily replaceable.

I like to play a proactive game, so although I see the value in the centaur, he rarely fits in my strategy. He's just too defensive and defensive is not something I like to be in Theros. Like rstnme, I've played my fair share of 3/5s for 5 in past formats, but in Theros, they just don't work for me.

Th asp is twice as good as the others.

I heard that the centaur is great with 7 toughness, underrated and underestimated but I never got to play it so it is all hearsay. I did play against it before though, and it is just annoying.

I like the fox, 6/5 trample is good. However, I have problems making it fit in sometimes. Still, the trample is really good, makes chump blocking hard. Trample is a nice asset to have in this draft environment.

Personally, I think the asp is the best green common fatty. 4/5 is solid and most importantly, it has reach. Reach. Saved me more than once already from fliers. In one game, I managed to get to a stand-still despite differences in numbers because of the asp and turned the match around with a Hopeful bestow and monstrosity activation.

The Asp comes out significantly ahead of the others, but Vulpine Goliath is remarkably difficult to stabilize against due to trample. I've had a grand total of 1 times that the Centaur was used against me to any significant effect. It stalls up the ground, but can't stop aerial threats, and is too easily chumped or even flat-out blocked.

What everyone said. Snake > Fox > Centaur(s). But I don't want to play more than 1 6 drop or more then 2 5 drops.

Usually Fox is competing with a blue flying 6 drop, and/or nemesis of mortals. If I'm not in UG I am happy to run a fox though.