SPOILERS
SPOILERS
SPOILERS
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SPOILERS!
The film will start with Finn participating in an Empire mission with Kylo Ren in command, massacring and burning down a village (Stormtroopers being deployed to a village in trailer 1, Kylo Ren at the burning scene in trailer 2).
The mission makes Finn start questioning his moral stance and he decides to defect from the Empire. Traumatized and with blood on his hands, he returns to the star destroyer and shoots up his former allies with a TIE Fighter (seen in trailer 2) and attempts his escape.
He gets shot down over Jakku (opening shot to trailer 1, most likely the same planet where the village massacre took place), and he is left to search for refuge on his own.
He comes across Rey, who found Luke's lightsaber in her scavenging (as seen cleaerly in the third pic below). Finn recognizes the weapon as that of the infamous Luke Skywalker, the legend responsible for crippling the Empire (know your enemy and all).
This leads Rey and Finn to seek out Luke after discovering that Rey has a connection with the force (and possibly the Skywalker family). They head to the trader outpost seen in both trailers. The Chrometrooper is hellbent on taking out Finn, and leads a ruthless hunt for him (almost satisfying the role of bounty hunter, only under the Empire's command). And so, we have the scene in which TIE fighters bombard the trader outpost with the intention of taking out Finn (trailer 2).
They steal the Millennium Falcon and attempt their escape from Jakku, with the intention of rallying with the Rebel Alliance in another system. Mind you, the pilot chsing down the Falcon utilizes chrome armor.
Upon escaping, they meet with the leader of the Rebel Alliance, Leia, knowing she's Luke's sibling and that she may be able to assist in seeking him out. They get Luke's saber in her hands and she recognizes it as her brother's, legitimizing Rey and Finn's intentions. Before sending them out to seek him (and unsure of Luke's mental state), she provides them with companions who have history with Luke: Han and Chewie. "Chewie, we're home" implies that Han nor Chewie have commandeered the Falcon in a long time, effectively busting the theory that Han and Chewie help Rey and Finn get out of Jakku (that would be a bit too convenient). This approach also enables the film to reunite Han and Leia in a way that makes sense. Also, I'll have to guess that R2 and C3P0 are under the Rebel Alliance's supervision up to this point, and they're also sent along with Han and company aboard the Falcon (just like old times).
Regarding Kylo Ren, I suspect he senses a threat to the Sith and the Empire, one linked to the Skywalkers (and we all know what happens when you pit a Skywalker against the Empire). He seeks out the remains of Vader, somehow trying to narrow down who this person (Rey) is. This might be an opportunity to integrate the much-rumored flashbacks (featuring Vader and the younger versions of Luke and Leia). Kylo then sets out to destroy this potential threat to an already-wounded Empire. He will serve as the endgame villain.
And regarding Poe Dameron, I think he'll be utilized as a rival to Finn (former Stormtrooper against a patriotic X-Wing pilot). It will make for interesting drama and nice contrast between the Empire and Rebel causes.
A stray and completely unsupported guess is that Finn will kill the Chrometrooper (Captain Phasma played by Gwendoline Christie) to complete his respective arc, solidifying him as a good guy when tempted by her to turn against his new friends.
Granted, we do not know who her parents are as of right now. Could she actually be his daughter or something? In that case, the speech which we hear about the force being strong in his family does make sense, but it's just speculation right now. 
