Good points made in posts:
1 keep the seals oiled; recommend a silcone spray, keep pressure on seals
2 there are a number of ways air rifles delivever their air, a break barrel uses a spring loaded piston which has a brisk small kick forward then backward, I can't hit much past 30yds with one and some quality scopes will simply break after some use on such gun. Of course some folks prove this wrong. If using a break barrel, hold loosely, don't grip tightly.
3 CO2 smooth shots but generally underpowered for rabbits
4 multi-pump rifles work well
5 pcp high pressure rifles work great, are the bees knees if you have more money for air rifle than a 22lr
6 safety, a falling 16gr pellet smarts, yet barely leaves a red mark on bare skin; a falling 40gr bullet can break skin, cause injury, or pit a hole/break glass on reentry; 25ft/lbs pellet vs 125ft/lbs subsonic 22lr
7 noise, power roughly correlates to noise, double your 'crack' at 1100fps due to sonic wave affect
8 power, a 17 pellet loses power rapidly, a 22 pellet at 13-15ft/lbs would be a desirable minimun for a bunny headshot (though perfectly placed shots much less) 18ft/lbs at muzzle doesn't deliver 15ft/lbs at 40 yds
9 pellet shape; do not use hollow point pellets (or pointy pellets) commonly sold at Walmart, unless shooting inside 30yds, even then, there's no advantage, further out they have a ruinous coficient, don't fly straight, and haven't the velocity to expand on shots past 5yds. Soft lead dome pellets best, crossman sells fine pellets not too hard to find.
10 match pellet to power, 20ft/lb rifle around 15gr; 30ft/lb magnum pellet rifle around 20gr
http://www.straightshooters.com/
If you have good credit and credit card check out this site; loads of great info.
Checking the bunny population, what fun!