I'm predicting Quarians are in ME:A. (Spoilers from the Gameplay Trailer)

The established timeline puts the Arks as leaving before the events of ME3. So no Geth, unless Bioware is willing to contravene their established lore again.

They don't have to. The Geth are easy to explain while keeping the lore intact. Either their involvement was kept secret because of public perception of them, or something as simple as a bunch uploaded themselves onto the ships. 

I don't think we'll have a Quarian squadmate.

Right now the squadmates appear to be PeeBee, Liam, Cora, Drack, the female Turian, and there is a rumored A.I. companion. That's six companions, which might be the full squad. If there is a seventh, I'd bet on an Andromeda native over a Quarian. I doubt we'll have more than 7 squadmates.

I'd be surprised if some Quarians weren't on the Nexus however.

Maybe the character in Engineer Adams' place will be Quarian this time around. We're getting a Salarian pilot, so why not a Quarian chief engineer? 

There was also talk that some species won't make the 1st game in Andromeda, so a good chance Quarians won't make it. In later games they may come. I think for now it will mainly be new and council races. And nb4 "what bout da krogans?" You need muscle and someone to do the heavy lifting. Quarian isn't going to be doing that.

Plus, we see in ME3 that if they stop shooting at each others, they can actually live in the same armour. I don't think that particular is to forget.

Highly doubt it. I don't think there is room, and I don't think we will have crew as big as in ME2. The core races are there, the aliens are there, we will manage without Quarians or Geth (a single one, since they haven't been friendly) for that matter. The Citadel races have the biggest presence, and they will make it to the team, plus probably a native character. There might be Quarians on the Nexus in small number, doubt they will make it to the Pathfinder team.

Oh, please no. I've had enough of those stun locking bastards for three games.

Even so, it is a safe bet that they are one of the fan favorites.

Companion characters become the avatars for their species, and fandom for those characters spills over to the characters' species. Players that like Tali are also usually fans of the Quarians. Fans of Liara or Samara usually like the Asari, Garrus fans think the Turians are cool, ect, ect.

I agree that the chance of geth being included are slim to none. I would think that if they do include AIs of any kind, they would be 'native' to Andromeda - as that would create a better opportunity for a fresh narrative than the geth. We've already gotten the geth's story. Though I love the geth, and Legion is a personal favorite, I don't particularly want to hear that story again.

Regarding the quarians, I've seen a lot of speculation that they won't be included. I'd be extremely surprised if that's the case. They spent a lot of time in the ME series building their lore and including them in the narrative. Tali is a beloved character. Hell, Reegar, who we talk to for all of five minutes, has his own little fan club And, there's plenty of good reasons for them to be involved in the project. No one is as good at salvaging and re-purposing technology as they are. They also have experience creating and maintaining self-sustaining ship communities. It would also be very easy to give them reasons to want to go. Continuation of their species and all that, especially with that big, extremely dangerous war they're planning...

I could certainly see them not including hanar, elcor, volus, vorcha, yaagh (not sure I spelled that right). But outside of the council species, the quarians and krogan are the most featured races. Again, it would be a very weird decision on the game creators' part to just leave them out, or even to just relegate them to background npc status. Even if we don't get a squadmate, why would they not include one as an important crew member? We have a salarian pilot, after all, so I imagine the whole crew will be a mix of species - which is pretty exciting in itself by the way. I'm not one of those human = boring types, but having a mix be would be fun. Especially since they'll supposedly have even more dialogue than our squaddies in ME1-3 did.

What is it with you and weird, arbitrary ultimatums?

When I 1st saw the squad mate icons it is pretty apparent that there is a turian one (that icon is butt ugly) and Asari one and one other that I immediately thought was an quarian face but after looking again probably not.