If you don't mind running your own (or can find a instance of it yourself ) tt-rss is a great RSS feed reader. After having google reader, and then another alternative I tried closed down, running my own seemed the best way to ensure I'd have a RSS feed reader I could rely on
- ads? What ads, you're running it yourself
- Categorization: as much as you'd like
- has great third party app support
- updates can be set per feed, but the minimum update time is 15 minutes.
- price - free/open source, though you may need to pay for hosting. I used to run an instance on a VM at home, and I currently run it on a VPS
Digg reader is probably the one you should go with if you're looking to a nice, ad-free non self hosted alternative. I didn't use it originally cause it lacked a few key features I wanted (For example hiding empty feeds and folders). Its reached the point where if I wasn't running ttrss, I'd run it, since I could tweak it into working for me
- no ads as far as I can tell
- folders for categories
Its still in active development, and I do believe they intend to reach parity with google reader pre shutdown
I've no idea how often it checks for new feeds
I used to use the old reader in the past - Unfortunately, when I used to use it, they had less restrictions and my needs are significantly greater than what their free tier offers. They also had capacity issues, and ended up booting off most of their users. I'm not angry that I lost a free service (Quite more that I was a little broken hearted, its a great app, but the uncertainty meant I decided not to rely on third parties). Its the closest in terms of features and usage style to google reader IMO, though its not completely free.
If you have less than a hundred feeds its free, with added plans for more feeds.