Danbo, you've got yourself a nice rig. Shoot it and enjoy it. Yes, you could spend more on RWS or Beeman. In return for the extra money you would get a nicer trigger and less vibration in the shot cycle, but you would not necessarily get better grouping ability. You've got a good tool for the job.
As far as pellets go, the gun will decide what it likes to shoot. The shooter never does. Break in the gun with 200 to 500 pellets (you know not to ever dry fire a spring piston rifle without a pellet in the chamber, right? You get damaging "piston slam" if you do and it's a matter of "when", not "if" you deform the chamber.
Next, get a pellet sampler from a place like this:
http://www.straightshooters.com/common/sspelsmp.html
This is the cheapest way to test 36 types of pellets without having to buy 36 tins. Shoot 5-shot groups at the distance you plan to pest control. Then all you have to do is go with the pellet that performs the best at that distance.
If you shoot only one pellet, you only have to learn one trajectory, you have the most accurate pellet for your gun, and life is simple.
Since a rabbit's brain is about 1" in diameter, you need to be able to hit this size target reliably. Set a 1" target at a distance you can hit within the circle 8-9 times out of 10. Keep moving it back in 5 yard increments until you can no longer reliably hit that target under field conditions. That is your real-world limit for pest control.
With head shots, your gun will have more than enough power to quickly and humanely take down rabbits further downrange. The limiting factor for a powerful gun like yours is always the shooter--up to what distance can you keep 8-9 shots in a 1" circle under field conditions.
You may find shooting easier if you hold the gun with just enough pressure to support it. Don't tighten your grip or try to stop the vibrations/recoil. This is the easiest way to hold the gun exactly the same each time you shoot it--which is very important for a spring-piston airgun. They are very hold sensitive, and the discipline you learn in consistently holding them and holding on target through the long shot cycle will make you a fantastic shot--of airguns and firearms.
Temper--there is a new FT class in the US called "Hunter Class". Most clubs now support it, and it's a "run what you brung" class that limits rifles and optics from getting into a technology race. I've shot with several hunter class shooters and they all enjoyed the game very much.