I have the 75-300 III non-USM version and most images coming out of it are completely useless. You are much better off using your 55-250 and crop down the image. If you had a bit more budget, I just recently upgraded to the Tamron SP 70-300 VC USD and it's absolutely incredible. That Tamron won EISSA and TIPA awards and is quite amazing. Canon's EF 70-300mm f/4-5.6 IS USM isn't far behind, but is a bit more expensive, so I would recommend the Tamron over it.
In all honesty, if you're looking for a 100$ telephoto lens, you're probably better off getting a 50mm f/1.8 and crop the image. The cheaper telephotos as the 75-300 III will just disappoint you.
And as was stated, with planes going that fast, you will be using a super high shutter speed (maybe 1/500 or 1/1000, maybe even more), so IS or non-IS won't really make a difference for this.
Cameras: Canon EOS Rebel T2i, Canon S90
Lenses: Tamron: SP70-300mm F/4-5.6 Di VC USD, Canon: EF-S 18-55mm f/3.5-5.6 IS Lens, 75-300mm f/4.0-5.6 III, and EF 50mm f/1.8 II
Retired camera: Fujifilm Finepix s700