Group one is three Stormtroopers who - inspired by Finn and tempted by promises from a prisoner - break away in the immediate aftermath of Poe and Finn's escape from the StarDestroyer. They steal an old Lamda Shuttle and book it away from the First Order, and head to Maz Kanata's place. The prisoner they escape with is a Holovid superstar who is ungodly famous, and is very sympathetic to the Resistance. In fact she held a big fund-raiser for the Resistance, which is why the First order captured her. She knows Maz Kanata, and says it's safe from the First Order.
The second group is two 'street Jedi'. One was a padawan in Luke's disastrous Jedi School, who escaped death but is running and staying low, and the other is a force sensitive who picked up an old light saber and is training herself. They have just arrived on Jakku looking for a Church of The Force which is supposed to be strong in the local villages on Jakku.
The third group is two scions of the old group of StarWars-ish characters, a young wookiee and a younger Twi'lek. They are here on Jakku because they heard about a StarDestroyer having crashed on this desert planet just behind a smaller ship. They think this is because of their parents, having both heard this story growing up, because... yes, it did happen with another star destroyer on another desert planet in our game, long before we heard of Jakku! They want to see this, because they never really believed the story.
The Twi'lek was also an escaped padawan of Luke's School, and yes, she knows the other ex-padawan. I expect groups two and three to merge the first day because of this. :D