I use shutter priority for air shows almost exclusively. The general rule of thumb is no faster than 1/focal length. That is a general rule, and I break it occasionally.
So if you have a 300mm lens, the rule of thumb is no faster than 1/300. That being said, it's what you are comfortable with. If you have a stabilized lens (IS for Canon, VR for Nikon), you can go lower with good results, but keeping a steady hand can be really helpful. My Sigma 50-500 is a non-stabilized lens, so I will usually shoot 1/500, but will drop below that if I feel comfortable.
When you shoot shutter priority, you control the shutter speed, the camera will adjust the aperture automatically for that shutter speed. Aperture priority is the reverse, you control the aperture, and the camera selects the shutter speed based on the aperture setting you have. The reason I use shutter priority is so that I can control the speed of the shutter and thus control the amount of prop blur I can get. The slower the shutter, the more prop blur. But that also has a risk of everything being blurred.
ISO with digitals is kind of a throwback to film speeds based on ISO ratings. There are a ton of differing opinions on it. I used to shoot 200-400 ISO at airshows but found that there is significant grain in enlargements at 400 with the camera that I use. I have since gone to ISO 100 for everything on my D80 and 200 on my D50 (lowest setting the D50 supports). You will have to experiment with the camera body you have to determine what the sweet spot it for ISO settings. Most newer cameras has high ISO noise reduction that can reduce the amount of grain at high ISO settings, but some do it better than others.
Shooting full automatic will net you some nice shots, but the problem with automatic is that you are trusting the camera to make the right decision, which for many shots is fine. But when shooting propeller aircraft on a bright sunny day will often set the shutter at 1/1000 or even higher. That will stop the prop completely. Maybe I am a control freak, but I like to be the one who decides what speed the shutter will open and close at.
When trying new settings, it's always best to experiment before you go to an airshow to get a feel for the settings before you spend a day shooting and get home to find your shots are over-exposed, blurry or not up to par.