People have all kinds of theories about pellets, flat head pellets for rats up close, pointed pellets for long range pigeons and round head for mid range rabbit etc etc.
Then you have the plastic skirt, steel head or wonder alloy pellets, forget about them all.
At the end of the day a good quality round head lead pellet is the best all round choice, find one that's readily available and that works well in your gun, buy as many as you can and practise with only those pellet's.
I have 2 x .22 and 2x .177 air rifles, i FT with one .177, HFT and a little hunting with the other .177.
The .22's are mid (18ft/lbs) and high powered (30 ft'lbs) guns and to be honest i like .22 better for hunting (even at 12ft/lbs) .
.177 is better at 12ft/lbs for FT because range estimation and pellet trajectory are all important but i like the stopping power of the bigger pellet when hunting.
Both will do the job, most important thing thing to do is practise and get to know your gun, scope, pellet combination really well.
Once you work out the trajectory and you are able to consistently hit say a 40mm circle then your ready to go.
I stick the trajectory on my gun or scope so i always have it to hand.
This is for a 12ft/lb AAS410, .177
LHS is range in yards next is the hold over or under in mm's