I know I'm way late to this thread, but I find it interesting that much of the advice given is counter to what I do.
Using first the 55-300 ED and later 55-300 WR, I shoot Av mode at f/11 and let the ISO ride up to 6400 on the KP. I think with the K-5 I'd let it up to 3200 and the K10D no higher than 400. I may also add up to +1 on EV but not always. And of course, I shoot in RAW. That's it. It's a slight variation on "f/8 and be there" that has worked a lot for me, both at airports on regular days and at air shows. Check my Flickr albums for results, though I notice I've not done an air show yet with the KP.
On the topic of prop blur, getting a full disc as suggested by one poster can be a mighty challenging task for a moving aircraft. Prop and aircraft speeds will vary widely but I recently made some calculations for a Bombardier DHC-8 turboprop, and the aircraft will have moved 2.5 m (over 8 ft) forward in the time it takes the prop to do one complete revolution! Even allowing for the 4 bladed prop, that's still 0.625 m (over 2 ft). If you're anything like close (as you likely will be at an air show) that presents a challenging tracking solution. Different aircraft in different flight regimes could be a lot worse or a lot better and you'd have to really know your aircraft to adapt to each one!
Here's the fastest aircraft at the last show I went to. Shot parameters are
f/11, 1/800, ISO 250. (That's one of the higher shutter speeds of the day. Looking at that section of the show — and thus relatively consistent lighting — they mostly range between 1/250 and 1/400, and all the props are blurred.)
Oh, and the reason for f/11 is that is where the ED lens was at its sharpest according to my testing. Recent testing I have done with the WR suggests it may do fine at f/8. And indeed I have some ED shots at f/8 that were fine.
When it comes to depth of field, I think you can pick anything you like. Again, a calculation I have done before. This shot is about as close as I can get to the runway at my local airport. The aircraft is shot slightly rear-quarter because it's tricky to fit it in at the 55mm wide end of the 55-300 when it's directly opposite. But let's assume the subject was small enough to fit comfortably. The runway centreline is approximately 113 m away, which is
close!
55 mm focal length, focussed 113 m distant, and let's say you're really lucky to be using an f/2.8 lens — your DOF (on APS-C) extends from 36.3 m to infinity. More than enough to get the entire depth of the aircraft sharp. What about a smaller aircraft that requires some zoom? A fairly tiny Cessna 152 has a wing span of just over 10 m. Zoom in to 300 mm with that same generous-to-light, depth of field-robbing f/2.8 and you'll get 7.5 m in front and 8.6 m behind for DOF. Again, more than enough. Given most of us aren't going to be using f/2.8 capable lenses you can pretty much pick any aperture you want unless you're REALLY close. If anything in flight is closer than 100 m you're probably breaking some law. Stuff on the ground, of course, could be much closer, but then you're likely to be stuck on much shorter focal lengths. That Cessna 152 will still be entirely in the 55 mm DOF when 20 m away, and yes, the 7.34 m long aircraft will just fit in the ~8.5 m field of view at the focus distance.
That's why I pick the aperture where my lens performs best and just go with it. Creative DOF isn't really an option in these shooting scenarios. Leave those considerations for the arty shots on static display aircraft.