Get a springer, just more fun imo.
The Weihrauch 99 (lightweight) and 77 (heavy) both come with open sights so great for plinking and short range target shooting as well as hunting.
If you don’t want open sights buy the one that feels nicest.
Air Arms, Weihrauch, Diana and Walther all make nice, quality springers.
No point in buying something cheap from an unknown brand, much more chance of it being a gun shaped object.
There are exceptions, Hatsan from Turkey are nice (and make Webley’s guns for them now).
Hawke and Nikko Sterling make nice mid range scopes.
Get one that’s adjustable for parallax.
Something like a 3-9 mag * 40mm is great for hunting, enabling you to focus down to realistic ranges.
You might want to go a bit longer, say 4*12 if you want to shoot targets at longer ranges.
And a rabbit’s brain is about the size of a 2p coin.
You just can’t risk a missed shot with an air rifle, the bunny will just go to ground and die slowly and agonisingly.
Your range should be limited accordingly.
It can be great fun, rabbits aren’t stupid and it takes a bit of skill to get close enough.
Wood pigeons are even harder – their brains are tiny and chest shots aren’t guaranteed to kill cleanly.
Prefer .177 myself.
Flatter, less affected by wind, cheaper and you can use it for target shooting if you like.
I used to enjoy hunting and everything apart from the rats got eaten.
Then we got a pet rabbit, I found out that wood pigeons mate for life and I became soft.