So I guess you are familiar with aperture settings, shutter speeds, ISO etc. For airplanes you usually want to try shooting (especially as a beginner) on sunny days with the sun somewhere behind you. Airplanes I always shoot in AV
(aperture priority) with my aperture set at 7.1 and ISO at 100 or 125. This allows me to maintain a shutter speed of either 1/800 or 1/1000. You want to photograph airplanes using a fast shutter to prevent motion blur. Once you get the hang of shooting in sunny skies, you can venture off to other weather conditions like cloudy days and all. For those you would have to open up your aperture more (lower number for the f value) and bump up your ISO a bit to maintain that shutter speed. You also may have to play with your exposure and metering to get the plane looking right. That is all more advanced stuff you will come to understand as you gain experience photographing.
I definitely think playing around at a camera shop is going to be your best bet. You want to find an SLR body that feels comfortable. Classes definitely are a good idea. With that said, I never took any photography lessons. I just played around with my cameras and read up on my own about things when I wanted to enhance my ability.