Thanks for your question, Rosie.
My go to tool for triggering ideas for an exploratory testing session is the Heuristics Cheat Sheet. An epic and snappy all-in-one companion. It just gives me a little nudge and reminds me, “Oh yeah, I could do that!”.
There’s also tonnes of useful tools on this thread.
Plus there’s the terrific TestSphere. It flips your brain into many different exploratory testing positions. And with such variety you tend to have more options available to trigger test approaches for a productive exploratory testing session.
When testing a web application my go to tools are Chrome’s developer tools, application logs and an excellent screen recorder that churns out GIFs, such as LICEcap. Super important to explore the Console and log output as you explore. The app might appear to be in good shape for the user but below the surface may lurk some problems. I also use my own tool for managing my testing sessions and capturing testing notes: TestBuddy.