I would recommend Downread.com, but that’s because I am the author. Fully on the web, no self-hosting, forever free for everyone who signs up as long as the current servers can handle it. Works well as PWA (apps coming soon).

The most common browser-based readers are Inoreader and Feedly. Inoreader has more features, but I prefer Feedly’s UI.

New on the block and still in beta but you can try Muuted. I built it myself. Muuted.com. Inoreader is solid too. It’s what I used before I built Muuted. If you'd rather self-host, FreshRSS and Miniflux are the usual picks.