Warning: Spoilers for all Game of Thrones episodes leading through the Season 6 finale.
Daenerys Targaryen, the First of Her Name, Queen of Meereen, Queen of the Andals and the Rhoynar and the First Men, Lord of the Seven Kingdoms, Protector of the Realm, Khaleesi of the Great Grass Sea, called Daenerys Stormborn, the Unburnt, Mother of Dragons, and whatever else is coming next season is officially on her way to Westeros.
Which means that her conquest of the seven kingdoms will be in full swing in about 42 weeks (give or take an episode). During the Season 6 finale it was revealed that Daenerys will sail to Westeros with a pretty open mind in terms of who she will marry to forge a powerful alliance, as well as which angle she'll swoop in from (perhaps Casterly Rock in the west is too far a journey?).
The Mother of Dragons has already fostered support from two out of the seven kingdoms: the Tyrells of Highgarden (Kingdom of the Reach) and the Martells (Principality of Dorne), evidenced by the Dornish ships we see in the end shot (while you were trying to figure out how Varys learned to teleport).
Out of the five kingdoms and wildcards that remain, which will fall in line with Fire and Blood? Let's evaluate the options, starting with the least likely.
1. The Lannisters — Kingdom of the Rock
Chance of alliance: Equal to birthing twins after chugging a vat of moon tea.
For obvious reasons, Cersei and Jaime Lannister will be the staunchest enemies Daenerys has to contend with, thanks in no small part to her newly-appointed Hand of the Queen. Now that Cersei is queen herself, she can resume her mission to avenge her father and son by eliminating Tyrion once and for all. As for Jaime, don't forget that he promised Bronn he'd kill Tyrion himself for murdering their father.
And even aside from all this family drama, Daenerys represents the clearest threat to the Lannisters' consolidation of power in Westeros.
To be fair, there is now a clear rift between Jaime and Cersei Lannister, so tinfoil theories can speculate all they want about a possible betrayal in which Jaime marries Daenerys by the end of the series; I just wouldn't put any gold dragons on that bet.
2. The Ironborn — Unofficial Kingdom
Chance of alliance: About as likely as another direwolf getting killed.
In other words, this could go either way depending on how the story between Euron Greyjoy and Yara/Theon Greyjoy plays out. Right now, the Ironborn are divided politically, even though Euron has the better part of their forces and a new fleet being assembled slowly but surely.
It's quite unlikely that Dany would bring Euron into the fold considering her own standards and existing alliance with Yara, though you could speculate that down the kingsroad, the Ironborn will fall in line simply to keep playing the game.
But in my opinion, it's more likely that Euron will either act independently as a new(ish) villain of the series or join forces with the Lannisters in order to stamp out his niece and nephew.
3. House Stark — Kingdom of the North
Chance of alliance: Hearing someone say "kingindanorf" next season.
I doubt it will happen right away, but Jon Snow and Sansa Stark have an uncomplicated motive to align themselves with the Targaryens. With Cersei as queen, war with King's Landing is all but an inevitability (Cersei still believes Sansa played a role in killing Joffrey).
The North will remember, but what grudge will they have against Targaryens? It was Robert Baratheon who had the most cause to dethrone the Mad King and defeat Rhaegar Targaryen. As long as Jon Snow bargains independence with Daenerys, the North will probably see more benefit in uniting against the Lannisters.
And of course, it's hopefully only a matter of time before Jon Snow learns the truth of his parentage, as revealed in the finale: He is the nephew of Daenerys Targaryen and the last of her living relatives on the show. Let's get this song of ice and fire started.
4. House Arryn — Kingdom of the Mountain and the Vale
Chance of alliance: Equal to your theory about Littlefinger coming true.
Who really knows at this point? Technically, Baelish is also the lord of Harrenhal, which ruled the Kingdom of the Isles and Rivers. But after the War of the Five Kings, the Freys essentially took power over the Riverlands (and then retook Riverrun), so we can just assume that Lord Baelish is only pulling the strings of Robin Arryn and his Vale knights, which is nothing to underestimate.
At first glance, it's easy to assume that Baelish will ally himself with whoever the North (and Sansa) chooses to get behind. But we already know that Littlefinger's only goal at this point is to rule Westeros for his own sake with Sansa by his side. Daenerys is an obvious obstacle for him to get through, so unless his manipulation over Robin Arryn is changed or finished, the Vale's alliances will be the wildcard for now.
5. House Frey — Kingdom of the Isles and Rivers/Riverlands
Chance of alliance: About as likely as us figuring out how face magic works.
Technically, it could happen, but it's a bit far-fetched. All of the Tullys are dead except for Edmure, who simply deserves to be dead at this point. And though Walder Frey and some of his sons have been righteously-yet-creepily murdered by Arya Stark, there are plenty of Frey successors ready to pick up the pieces.
The firm hold the Freys have over the Riverlands will probably be challenged by the North in the coming season, while Targaryen forces do battle with Lannisters in the South. In other words, the plot needs a bad guy above King's Landing.
A few things to keep in mind, though, if we're gleaning some info from the novels: The Frey succession is a violent, complicated matter because it's been hinted that they will fight among themselves over who is the rightful heir to Walder Frey, especially now that his central leadership has been baked into a pie. So it looks like even the Riverlands are up for grabs, assuming House Blackwood and the Brackens are still in shambles.
6. House Baratheon — Kingdom of the Stormlands
Chance of alliance: Equal to Gendry ever showing up again.
We want it to happen, but the show has spoken. Now that Tommen Baratheon is dead, the ruling House of the Stormlands is legally extinct. That said, the region and its forces who didn't follow Stannis are still intact and under the control of King's Landing.
So we can probably expect the lingering armies of the Stormlands to be ravaged by Daenerys Targaryen for dramatic purposes. They don't stand a chance against the united forces of Tyrell and Dorne, let alone the Dothraki, Unsullied, and rebel Ironborns.
It looks like the War for Westeros will be a somewhat even match. It's Targaryen, Stark, Tyrell, Martell, and some Ironborn vs. Lannister, Frey, Stormlands, most of the lesser houses, and most of the Ironborn. As always, whichever wind the Vale blows will probably determine the winner.