Honestly, I think we have enough info now through concept art and game models to make a pretty good guess at our 9-10 companions if we assume every character that shows up in that bottom picture will be a companion.
Warriors:
Cassandra
Older Ex-Grey Warden
+ (Iron Bull)
+ (Mr. Moustache/Trident Guy)
Rogues:
Sera
Varric
+ (Scribe Girl)
+ (Cole)*
Mages:
Vivienne
+ (Bald Elf)
* = Except for the leaked survey and reports of an Asunder character being a companion, we've got the least evidence for Cole. I'm thinking he'll be a day 1 DLC companion.
I put parenthesis around all of the characters that we haven't actually seen in the party via gameplay footage, so they're really just speculation on my part, including their classes. Honestly, though, the ratios work out pretty nicely. Similar ratio of humans to non-humans as DA:O, and 5:4 males to females (when you remove Cole as DLC). The class ratios could be off, but again, that's just me trying to make it work neatly without actually knowing anything.
As for companion speculations, I have a few things to say:

Firstly, Mark posted a WIP model similar to that of the "Bald Elven Mage". However at most, this only confirms that the guy has an in-game model.

Iron Bull's concept art and in-game model. This does not mean that he'll be a companion 100%.

A closer look at the "New Home" concept art by Matt Rhodes. The guy in the red square has a different clothing than the Inquisition soldiers around him in the picture. Also, the fur/red cape looks similar to the templar from survey art.
DragonAging reports that David Gaider is writing two companions, Cassandra and an unknown one (I have not been able to find the source for this. If anyone knows, please send me the link). Recently, DG said that he has written two romance plots for DA: I. I think that at least in the previous titles, the writer responsible for the companion is the one who writes their romance arc as well. If that still holds true, we can assume two things:
1- Cassandra will be a romance option (
)
2- Watch me deduce: a-DG is writing two companions. b-The two companions are romance options as well. c-DG has already said numerous times that Cole won't be a romance option if he's ever included as a companion (with quite obvious reasons as to why that is). d-If Cole is in the game he will most likely be written by DG. e-Therefor, Cole most likely wont be a companion.
(Edit: Traditionally, DG always writes male romance options. And snarky/deadpan-y types as well. Who are you writing, David?!)
Heads up that there are big spoilers for Dragon Age: Asunder starting from here.
My list (just in case, everyone: note that with the exception of the three confirmed companions, everything else including race/gender/nationality is pure speculation):
Warriors:
Cassandra (female, human, Nevarran)
Grey Warden (male, human, possibly Fereldan or Orlesian. I vote for Fereldan.)
[*Templar/former Templar (male or female, human, unknown. Likely candidates are Cullen and Evangeline.)]
Rogues:
Varric (male, dwarf, Free Marcher)
Blonde Elf (female, elf, possibly an Orlesian city elf)
[Scribe Lady (female, human, possibly an Orlesian of Rivaini descent. Maybe a bard? Either way, I think she won't be a mage, as two Orlesian-of-Rivaini-descent mages are a bit redundant.)]
Mages:
Vivienne (female, human, Orlesian of Rivaini descent)
[Bald Elf Guy (male, elf, Dalish or former-circle-mage-turned-apostate)]
[**Rhys from Asunder (male, human, Orlesian of Fereldan descent former-circle-mage-turned-apostate)]
To make the above list less cluttery:
[Fancy Facial Hair Guy (male, human, Orlesian. See footnotes though.) Can be either a mage due to the trident thing, or a rogue due to having a sword as well. Wanna know what wild theory I came up with? He could be Cole, wearing Lambert as a suit. Veeeeery unlikely though, as that would jeopardize interactions with Cassandra, and really, what use possessing Lambert's dead or alive body would have for Cole?]
[Iron Bull (male, qunari, unknown Tal-Vashot). Either a warrior, or a rogue which would make him even more of a different approach than that of Sten.]
[Cole. I already gave my reasoning for why he might not be a companion though.]
There is a possibility that we'll get a 10th companion in the form of DLC. It could be anyone on that list, Cole, or someone else entirely. What I think we know is that the class ratio of the base game will be 3:3:3, as there has been talk of having four-member-one-class parties.
And now, the touchiest subject of all: romance options! Hmm, let's see. What we most likely won't get is a bit easier to determine: we won't get a qunari romance, Varric romance (well, there'd be lots of retconning involved otherwise), and the Grey Warden romance seeing as he's an "older guy", and possessed/spirit/non-humonoid romance. What we will most likely get is at least one male human and one female human option, at least one elven option, and at least one mage option.
Candidates are:
Females: Cassandra (semi-confirmed rumor, lol), the Blonde Elf, Scribe Lady
Males: Bald Elf Guy, male Templar/Cullen (if he's a companion at all), Fancy Guy (provided he isn't Rhys or even Cole)
But in the past, we always had a female mage romance option, so who knows, Vivienne could be an option? Her Valentine card makes me very doubtful though, lol.
Notes (
):
* I think there's a need for a Templar view point and one that actually shares either of the two extreme viewpoints in the order at that, probably the more moderate one of the two. Hence why I suggest Cullen or Evangeline. Though Evangeline would tilt things even more in the mages' favor, which would unbalance things even further.
** The first time I saw him, I thought Fancy Facial Hair Guy is actually Rhys. His appearance doesn't quite match Rhys' description, but that kind of stuff is prone to change. Nor does the sword he wields in the survey art match with, well anything really.
*** Rhys and Evangeline will go hand in hand, literally and figuratively! I don't think either will appear without the other, which reduces the chances of them being party members. It'd be cool if they are though, as that would give an interesting dynamic to the party's interactions.
*** It just occurred to me that all of the speculated female companions are young, and either human or elf. It was the same for DA 2 as well. That's... a bit disappointing.
**** I think the three mages would provide for the viewpoints that most mages have on the mage-templar war: Vivienne is a circle loyalist, Bald Elf would be all for mage freedom, and Rhys will be the moderate take-a-third-option viewpoint.
***** It also occurred to me that having three human warriors are a bit redundant as well. Odds are looking in favor of Iron Bull being the third warrior.
****** Just for fun:
David Gaider is writing: Cassandra, Unknown Companion
Mary Kirby is writing: Varric, Vivienne
Patrick Weeks is writing: A male companion, possibly LI as well? These are only rumors though.
Luke Kristjanson is writing: Blonde Elf
Sheryl Chee: Unknown
Sylvia Feketekuty: Unknown
Jennifer Hepler Had: One companion, who is either given to someone else to complete, or scrapped entirely.
Total Count: 6 out of 9.
I imagine Sheryl has 2, and Sylvia 1. Could be wrong though. DLC remains to be seen.
Thanks for all the awesome screenshots, Terrian!
You're welcome!
Edit: Words. I can spell you, words!
Edit Edit: God, what the...?! Logic, where you be at...?!
Edit Edit Edit: In other words, nothing in this post makes sense!
Edit x4: Stuff...
Mega-edit: Oh come on...