When it comes to longer lenses, there are three ways you can go. You can go with a consumer lens that starts where your current 18-55 stops, ex: 50-200, 55-250, 55-300, etc. These are normally less expensive, require changing lenses and have a variable aperture similar to the 18-55, but do not weigh as much as the the following. An all-in-one, which has focal length of 18-200, 18-250, 18-270. These are variable aperture consumer lenses where you will not have to change lenses as often because they cover the focal length of the 18-55 (you could leave the 18-55 home). These lenses tend to be slightly heavier and at the long end, tend to have a smaller aperture (exception is the 18-200 which has the same). This means the long end 250/270mm will have smaller (6.3) aperture, meaning the lens will not work as well in lowlight. The third option is what is referred to as fast glass or professional glass. That option would be something like the 70-200 f2.8. This lens will be more expensive and will weigh considerably more than the consumer lenses. All these lenses are produced by your manufacturer or a third party manufacturer (Sigma and Tamron are the two biggest). The third party lenses tend to be cheaper. Whether to purchase OEM or third party is a hot button topic, so for this discussion, I don't want to go down that road.
The Canon shooters can recommend the specific lenses or maybe a fourth option. In my particular case, I have gone down both roads. My DW is also a photographer that likes to go light. She chose the consumer lenses (18-55 and 50-200) that are made specifically for the APS-C cameras. I chose the faster glass option and since my manufacturer did not make the specific glass I wanted, I went with a third party manufacturer (Sigma). I have the 28-70 f2.8, the 70-200 f2.8, 100-300 f4 and the 30mm f1.4 (this is my dark ride lens). I also have the weather resistant version of the consumer 18-55, primarily used as my wider angle option or in bad weather conditions when I need the weather proofing. I will add that these lenses are not just for Disney, but also are used in my other photographic life of motorsports. A lot of thought went in to putting this kit together so I didn't waste time and money buying multiple lenses for the same thing.
These are just some of the choices, maybe others can come up with additional and more specific options. Good luck and have fun.