Springers are a great starting point. I would stay .22 or smaller. A .22 is very versatile and has plenty of power for Rabbit and smaller game. My experience with .25 springers, tho I have not purchased one in a few years is that they have limited power for anything but the lightest GTO lead free alloy pellets @16.5g. Those magnum .25 cals also eat scope guts for lunch. Even Springer rated scopes tend to last only a few thousand rounds. So, a PCP would be the next option. Once you shoot a PCP you will be done with springers, well 95% of the time anyway. But, PCP's need air, lots of air. So you need an air source. Air sources, Hand Pumps, Air tanks, compressors all have advantages and drawbacks. Hand pumps take lots of effort and time to refill a gun which makes a great cardio workout, but when It came time to shoot, facing the thought of hundreds of powerful strokes of a hand pump for a few shots caused me to skip shooting. So I got an Air-tank. The word on the street was a scuba shop or a Paintball shop or a fire station will fill them to the required 4500psi Max. Well, maybe. Go to the shop you have in mind and talk to them first. My SCUBA shop could fill it, and did, twice. The next time they were out of Air, the next they needed me to leave the tank for a while and they would get to it when they could. So I tried the Paintball shop. The first time was no problem.The next 2 times, the Operators were not comfortable with the higher pressures. I was frustrated and didn't even try the firehouse. Depending on someone else for your air after laying out $700 for a tank puts a damper on your hobby. So I bought a compressor, one capable of filling my large tank, since I already have it. I can top off my own tank in my own garage and shoot thousands of rounds whenever I want. There are smaller compressors on the market that are cheaper and designed to only refill small tanks, such as those found on rifles. If you get the smaller compressor, look at a small pony tank that can be filled while you shoot. a rifle that has a 50 shot capacity sounds great, till you have to wait 15 minutes for the smaller compressor to refill the rifle. A pony tank can be topped off while you shoot so you can top off the rifle in seconds.
Bottom line. If your rifle is for taking out occasionally, stick with a quality springer. If you want to shoot often a PCP is the way to go. Good luck, it is fun either way.