While Microsoft is putting up a heck of a fight with Edge – the rejuvenated, rebranded Internet Explorer – and Mozilla's Firefox is a competent, memory-friendly browser, we still find ourselves recommending Google's Chrome browser over any other.
It's super-stable, highly compatible, and comes with a huge catalogue of free extensions to fully customise your web experience or intercept security threats. Signing in to it with your Google account means your bookmarks, browsing history and personal configuration will move with you to whichever machine you're on.
Chrome's key feature is one you won't necessarily see: it runs each of its tabs in a distinct memory space, meaning a crash in one won't take down your whole browser. This isn't necessarily friendly to machines with small amounts of RAM, then, but Chrome is still the best browser around.