TweetDeck allows you to view multiple timelines in one easy interface. You have the option to have open multiple columns (notifications, home, trending, lists, etc.)
The one that I want to stress the most is the creating lists in Twitter (click here for how to create lists). If you create lists you can instantly see the accounts you want to see the most. In the example below I show adding the list EdTech that follows Richard Byrne, Tony Vincent, Eric Curts, and Google for Education).
Embedded below is a 1 minute and 40 second YouTube tutorial.