Most Web Designers, as well as UI and UX designers, are using applications like Sketch, Adobe XD, Figma, InVision, and other similar ones today. To answer your question, you should use Photoshop for photo editing and Illustrator for drawing vector graphics. Photoshop and Illustrator come with a lot of unnecessary features that Web Designers never use. Plus, there are many features that come with an application like Sketch that Photoshop and Illustrator simply do not have.
If you understand Photoshop and Illustrator, learning Sketch or XD is very easy to do since most things remain the same. Note that Sketch only works on Apple products.