Once you login to Twitter how much time do you spend in reading or scrolling through the tweets which appeared after your last visit to Twitter? Definitely considerable amount of time! Why not have tweets or retweets from person whose tweets you usually read or click the link he shares? Tweets from such of your 'Following' will go to Priority Tweet Box. You'll have the option to remove its mark as priority; from next time his tweets will not go to priority box.
For very initial analysis the app will consider links in tweets which you click to decide priority. You can manually also mark a 'Following' as priority. All his tweets will land in Priority TweetBox!!
Extended fun and ease with Twitter!!!