Janetter is a feature-packed Twitter client for iOS, Android, Windows and Mac.
The program supports multiple accounts and timelines, displaying tweets in real time, while pop-up notifications ensure you don't miss anything.
If this gets too distracting, you can hide some users temporarily or permanently, maybe hide tweets which contain certain words or are posted by defined applications. You can also come back later and easily browse through unread tweets, even if you're offline (thanks to a local cache).
There's support for displaying thumbnails of images, and of course you can tweet pictures yourself.
Janetter also supports shortening URLs, autocomplete, translations and more, and if you don't like some aspect of how the program looks or behaves, there's a very good chance it can be reconfigured.
A solid and reliable Twitter client with a good feature set.