DSLR certainly. Minimum 200mm lens, in addition to whatever lens comes with the camera, but preferably a 70mm-whatever mm zoom lens you can afford. Make sure you buy a good sized memory card and spare batteries. Even lower end DSLRs have reasonable video today but still shots are often more dramatic and you can take a burst sequence.
In over 40 years of aviation photography I've never used a tripod except for the odd static night shot and, at one month short of 69, can't see why one would be advantageous. Consider looking at a good processing program such as Photoshop, or Photoshop Elements for stills. There are also some good cheaper ones around. For video, Windows has a video manipulation program but there are many others available.