It depends on what you plan on using it for, distance of shots and where you will be using it. For small birds inside of stores, a .177 may be ideal or it may be overkill. If you're planning on using it outdoors for 20 - 30 yard shots on birds and small rodents, it's hard to beat a .22. If you plan on shooting larger animals at long distances (40 - 80 yards) such as raccoon, groundhog, or coyote you should be looking at .25, .30 or .357/9mm. However, if you're just looking for something to put down raccoon in cage traps with, any air rifle that generates more than 15 foot pounds of energy (FPE) at the muzzle will do. This link shows a skunk being dispatched by a .22 caliber air rifle producing 34 FPE
https://www.youtube.com/watch?v=4wx76H0DgEo&list=PLDGLNVzElHuasgtcqiwGjhPXDoMyRXzN0 although not that much FPE is required for one.
The most important item with an air rile is accuracy with the second most important feature being FPE at the point of impact. In other words, if you can't hit the vital area, it doesn't matter what you're shooting but once you can hit the vitals you need enough energy to quickly put the animal down. Accuracy is effected by many things, but too fast of a velocity is probably one of the greatest culprits. Pellets traveling 1100+ FPS (give or take) will destabilize based on distance, so you need to try different pellets at different distances to see what the air rifle prefers and what the maximum shooting distance is (my criteria is 5 shots in a 1/2 inch circle or less).
Once you've looked at the above questions and determined your answers, then you can look at the different power plants and their pros & cons to make a decision. PCP's cost the most and require additional equipment, but they tend to be more accurate than spring/gas pistons because the spring/gas piston power plant have bi-directional recoil. Multi-pump air rifles are a PCP style that have a built in pump so while you can control the velocity based on the number of pumps, you also have to pump between each shot.
Personally, I use a combination of air rifles in multiple calibers and power plants as I can't say that 1 air rifle fits 100% of all my needs. On the flip side, I will say that I feel it is more important to own and use a chronograph if you're planning on using air rifles frequently as that is the only way you will actually know the velocity and FPE each rifle/pellet combination can do