I've been having a go with the experimental web browser on my Kindle Paperwhite. I was initially put off because I found it very fiddly to use, but I'm getting more used to it now, and I've also found a number of resources that make the experience more bearable. The Kindle Paperwhite is not the best web-enabled mobile device around, but the WebKit-based browser is workable at a pinch (a bit like the ZX81 of personal computers), if you're away from home, at a public wifi hotspot, or if you just want to get away from your desktop and have not been physically or psychologically chained to your desk.
I don't think it's advisable to use the Kindle Paperwhite's experimental web browser for really sensitive or important work, such as online banking.
Wayzon Purple High Capacitive Soft Rubber Tip Touch Screen Stylus Pen Suitable For Amazon Kindle Paperwhite Tablet" at £2.45, but there are many others to choose from. You may prefer one with a finer, less blunt tip.
The stylus is fine for tapping on the keyboard, on hyperlinks and on buttons, though there are times when you have to zoom in to the web page content to pick out one closely-spaced link or button from the next. Clusters of social media sharing buttons are the worst, or buttons right at the edge of the screen. These styluses (or styli) have a soft rubber tip, so I'd advise that you use them for tapping and use your fingers for swiping and scrolling, if you want your stylus to last.
Tapping the screen
You'll get best results if you sharply tap the screen with your finger or stylus, rather than push. And when typing, allow a little time for key taps to register, as the Kindle's response to touch can be a bit sluggish.