I don't know if one of the superzoom bridge cameras is going to work for you, because the autofocus can be quite slow with these cameras, as can the time from squeezing the shutter button to the point that the shot is actually taken. This delay is often accompanied by the viewfinder/screen blacking out or freezing. You will need to find one of these cameras with at least a 900mm equivalent optical focal length. Digital zoom will not work for this.
When it comes to this if you go with a DSLR then you will be fine with any of the APS-C bodies. If considering Canon that would be any of the current Rebel series cameras upwards. When dealing with aircraft they are pretty predictable, so you don't need super advanced AF systems to track them. That is the "good" news, since they are the cheaper bodies in the range.
When it comes to lenses though if you are really limited to around 880 yards for light aircraft then you will need to be shooting with a lens that will allow you to have a focal length of 600mm. This focal length, along with some potentially serious cropping will allow you to get the images you want. I shoot airshows here in the UK at the sorts of distances you are talking about, using a lens of 600mm, and an APS-C, and I often need to make a 1.5× crop. Probably the best lens for this use is the Sigma 150-600 C, the lens I use, which is the cheapest option with Mode 2 optical image stabilisation that allows the operation of the lens stabilisation while panning. The Tamron 150-600 G1, which is the same price as the Sigma here in the UK, but I think a bit cheaper in the US doesn't have a panning mode of it's VC system, so if it detects panning it disables the stabilisation.
The big drawback of these lenses is the size, weight, and cost. The Sigma is £800 here in the UK and I think about $1000 in the US. As far as costs go there is another Sigma option, the 150-600 S and the Tamron G2 version, both of which are about $1000 more expansive. In the general scheme of things these lenses are actually very cheap, since the closest Canon lens is the 600mm f/4 L IS, which is a $12000 lens! Even the Sigma 150-600 C, which is IIRC the lightest of the 150-600 options is a big heavy lens weighing something like 3-4 Kg. It is also over 100mm in diameter. It is not possible to get a lens of this focal length into a smaller package.
Even with a suitable camera and lens you will still need quite a bit of practice to get good shots of the aircraft. One issue you will be dealing with is that for aircraft with propellers you really need to limit the shutter speed to at most 1/200s to get an acceptable amount of prop blur in the image. Landings are the worst for this, since you are usually at or close to minimum revs. It is much better if you could shoot at speeds of 1/1000s or faster, but those sorts of shutter speeds, most would say that on an APS-C camera you should shoot at that speed as a minimum when hand holding because of camera shake. Although good for sharp images it will also freeze the prop dead, and shots like that are very off putting and unnatural looking, especially to pilots or others involved in aviation.
All I can say really is like Frank suggests is get closer. If you can get within say 300 yards or so of the runway then you will be able to move down to a smaller lighter lens, like the new Sigma 100-400, which is much smaller and lighter than the previously mentioned lenses. But htis is still relative, since none of these lenses are small or compact. The laws of optics just will not allow for small lenses in these focal lengths.