I agree with Joe Spares in a previous post.
I use a Nikon L810 bridge camera, had it about 3 years now. 26x zoom.
I carry it when travelling. I have used it extensively at Frankfurt for example, and for taxying and static shots no problem. Very handy also for museums and scenic shots etc. However, for the airshow fast moving subjects and say, the 'Mach Loop' type shots, forget it. It would be very hit and miss, with the emphasis being on the miss.
From pressing the button to the shutter actually activating takes too long. It produces crystal clear shots, when used on the right subjects ( the NIKON Lens is excellent)
So I went DSLR and have a couple of Canons now. You can get some good deals on used DSLR's on ebay or Amazon and then find lens's in the same way. I have a budget and I managed it ok, so very much worth considering.
Canon EOS 450D
Canon EOS 750D
Nikon L810 Bridge/Compact.
Sigma APO OS DG 150-500mm