I have no problem controlling noise but Twitter seems incapable of delivering the signal. It seems impossible to have it show all the content from people I follow; instead it delivers some seemingly random subset.
As I was digging I found that Twitter started an algorithmic feed a while ago, and they optimize some metrics for interaction in order to show you the posts which are more relevant to you. IMHO, any form of feed filtering is prone to do unwanted things unless it can be explicitly controlled (Google+ was a good example of giving users control over their feed, but it didn't take off). The metrics optimized to decide which post to show or not show can never be completely correlated with user interest, that is one of the dangers of optimization.
Luckily for you, the people at Twitter have added a way to opt-out of the algorithmic timeline. Go in your options and uncheck the "Show best tweets first".
I did that when that particular change was announced; it still doesn't show everything and still often differs between loads. There should be a simple per-account selection of tweets, retweets, replies, and likes.
