My idea:
You create a Pred, set, roll attributes and choose class. (think spear master etc)
You can buy more weapons,armour,vision modes,etc on the mother ship, to buy weapons you need Honour points, to get honour points you have to hunt the most honourable targets (so say a small man with a pistol won't get much, whereas the big beefy man with the assault rifle is a good thing to go for)
The storyline missions are activated like GTA, small mission markers on different planets.
Earth is obviously the main planet where the main storyline takes place.
Other planets include sentient aliens and such, some need special vision modes, say they're cold blooded what do you do? Get the special vision mode for them etc.
Think of it set out like Destroy all humans just bigger, Earth has like 6 different countries you can visit.
Some planets may be too harsh for a predator to hunt, say, a below zero planet (Specialised armour comes in handy)
Just some basic ideas really.