What was the purpose in sending the Phoenix group through the portal?
It was an attempt to take over Terra Nova. There is a faction in the future that wants to exploit Terra Nova. The initial assumption is that they want to exploit it for natural resources that the future needs, but we see that is not actually the case. Instead, they want to exploit it for things that are rare/non-existant in the future (i.e. the dinosaurs). Which leads to your other question:
What was in the badlands that they wanted so bad?
It was another fracture. They sent a team out there to retrieve the piece of the ship which proves there is another space-time fracture that connects the future to Terra Nova's world. The ship was from a few centuries ago, which means it's not native to Terra Nova's world, it must have fallen through another fracture. This is why the Phoenix Group fled there upon their defeat. There are two places they could get reinforcements from the future, the fracture near Terra Nova, and the one they discovered in the Badlands.