Perhaps check out Matter[1] or Readwise[2]? I haven't actually used either myself (Matter requires an iOS device, though once installed you can also use a web app; Readwise was in private beta when I was first looking at it, but I think is opening up access now/soon). But they look nice. I used Feedbin[3] previously but found the mobile web interface a bit frustrating (I kept accidentally swiping things while trying to scroll).
[and the self-promo bit] I've also made one called Yakread[4], however it is quite unusual and won't be for everyone. Re: your requirements: it does 1 (via integration with pocket/instapaper) and 3 (it's a responsive website at least, no native app) but not 2 /exactly/. It has a home feed which is driven by a ranking algorithm, which is intended to solve the "too many newsletters/bookmarks clogging up your reading" problem, but might be a heavier solution than what you're looking for.
[4] https://yakread.com/ (see also https://tfos.co/p/introducing-yakread/)