Hi Silent, welcome to the forum
Personally, I'd consider the 35mm f/1.8 prime or a 50mm prime. If you want to learn more about photography, I think thats the best way to do it. The 35mm taught me a lot...
For planes, you're going to want something long. At least 200mm. The Sigmas tend to be the cheapest - the
70-300mm OS is less than £300 and is image stabilised. If you want really cheap, the
Tamron 55-200mm is only £105 (although I would avoid it personally).
If the 16-85mm is way too expensive, you're options are going to be limited...