I already had a Gamo "shadow 1000" and I really like it. It's accurate, shoots at advertised speeds and is cheap to buy. For my next air rifle, I wanted to step up a bit - so I settled on the RWS Diana 350 magnum in .22 caliber.
I chose well as the RWS 350 is the air rifle I'd always wanted. The cocking effort is a tad high - but I can use the exercise and that's where all the power comes from. By contrast the .22 caliber pellets move about 100 FPS slower (measured about 1 foot from the muzzle) than the .177 cal pellets. Pellet weight has a great deal to do with velocity - so find what you gun likes and accept that as "as fast as your gun shoots".
Speed is nice but for me I need a "tri-pack" of speed, accuracy, and retained energy. Selecting and testing pellets is crucial and I have a small network of fellow air-gunners where we swap pellets around. The best pellets for the money are RWS (hands down) and Beeman used to run a close second but their quality has fallen off and I've seen Crossman brand pellets that were more uniform and accurate than current Beeman pellets.
Buy a small 10x jeweler's loupe and keep it with you when you shop for pellets. You will be amazed at what you see. My favorite pellets in .22 are the RWS "Hobby" and "Superpoint" along with the extra heavy Logan dome pellets. For .177 I like the vintage Silverjet (but current production ones SUCK). I also like the RWS "Superpoint" and the Crossman "Hollowpoint" are surprisingly accurate.
I've shot all the trick pellets from solid ball, to plastic-skirt, PBA, and embedded penetrators. The best thing that trick pellets do is break the sound barrier as the PBA cracks about like my Ruger 10/22. Other than that - I say don't waste your money on them. As mentioned, my friends each all buy a tin of the trick pellets and pass them around. The best of the unusual pellets in our pass-around has been the .22 Logans that I stumbled onto via mail-order. Those should take rabbits no problem as they hit very hard and are accurate to boot.