Pellet Rifle .177
Pellet Rifle .177
US $29.99
What would be the best air rifle pellet for hunting rabbit?
Bear in mind i am in the uk and the legal limit is 12lbs in an air rifle (i think)
.177 or .22
Normally I like to recommend .22 caliber for hunting since it tends to deliver more energy in magnum airguns (think 20+ ft-lb guns), however there's really not going to be that much difference between the two calibers in a 12 ft-lb rifle. .17 caliber pellets have a higher muzzle velocity and shoot flatter. They also lose their kinetic energy quicker. .22 caliber pellets have a lower muzzle velocity and more pronounced trajectory, but they retain energy better at longer ranges and create a wider wound channel. Both are perfectly capable of killing rabbit out to 40-50 yards in a 12 ft-lb rifle provided you properly place your pellets (make head-shots). The issue will be placing the shots. Accuracy will probably limit your maximum range more than power since odds are that beyond 30-40 yards you'll probably find consistently keeping all your shots in an area 1-1.5 inches in diameter (roughly the size of a rabbits head) difficult. I think in a 12 ft-lb or under rifle I'd opt for .17 caliber since it delivers equivalent power levels, the ammunition is cheaper, and there is usually a greater selection of pellets and guns available. However its really a matter of personal preference. I'm going to link you to a UK airgun hunting site's comparisons between .17 and .22 caliber, 12 ft-lb pellet guns since it might be relevant to your situation.
As far as which pellet to use, you should use the pellet which your gun shoots most accurately. Most small game animals only take 2-5 ft-lbs of impact energy. The catch is that to take small game you need to precisely place your pellets for head-shots since you don't have the massive safety margin of a .22LR rifle (100+ ft-lbs) or a magnum .22-.25 caliber pcp airgun (40-80 ft-lbs) delivers. And since the differences in terminal performance aren't going to be that significant, you're better off with the pellet your gun shoots most accurately since it maximizes the energy your gun has.
The best advice for finding the pellet your gun shoots best is to get a couple sampler packages and try as many different varieties as possible until you find the one that your gun shoots best.