This is not as simple a subject as one might think. I assume you will need things to be portable per your comments. You and I are a lot alike so I will post my experience of doing similar activities for quite a while. My first thought on things is, are you going to go to multiple air shows or more importantly do you plan to change frequencies frequently?
If the answer is yes, then I assure you that you will want a scanner that you can program with a PC. Keyboard entering frequencies can get old very quickly. If this is the case then you should look at the aforementioned Uniden 125 (even with its slight limitation), Uniden 396T/396XT/352 line. I use a 396T and its far easier to create files using software for the various air shows I go to (Chicago, Oshkosh, etc..) than my other scanners outlined below.
If you want a dedicated or semi dedicated portable scanner for air shows, among the best I have used are the Radio Shack Realistic PRO-43 (200 Channel memory) and the Yupiteru 7100 (1000 memories). Both of these portable, are older and have their own health issues but are about the best you can get for civil and milair listening.
The PRO-43s' Achilles heel is its keyboard. They tend to stop responding after a while. There are articles online to help restore some of the keyboard functionality. I was able to buy several keyboards from RS before they went out of stock but the are all but unobtanium now. Also, some of the 43's had speaker issues as mine does. I use earphones or a mobile speaker and these work just fine. Also be aware the the previous owners may not have been as nice to their units as you might be. They may need to be aligned to get optimum performance out of them.
The Holly Grail in portables in my mind is Yupiteru 7100. This unit was not sold directly into the US as they do not have frequencies blocked that were previously used by Old Cellphone services. They are more a receiver than a scanner as they can receive HF frequencies in AM is SSB too. The audio output is strong and clear. The units are very sensitive and have a large memory, although you have to manually program it. You can acquire these on EBAY and other sites. The 7100's Achilles heel is it memory capacitor and these go bad causing the memory to become volatile. You will turn it on one day and all your memories will be cleared, quite frustrating! However, if you are handy with a soldering iron, replacing the capacitor is quite easy.
I might also add that if you are a ham, you might consider something like the Kenwood TH-F6A handheld. Yaesu and Icom also make HTs that cover the MILAIR and Civilair bands as well. These work great at airshows because the proximity of the aircraft to you. Which brings up the last point.
Antennas are critica for what we want to use the radios for. I recommend was the Diamond RH-77 antenna. They work great for both bands you want to monitor.