I was told long ago that the best thing I could do after I signed up on Twitter.com is leave the site alone and use other Twitter clients instead. There are many other programs and tools that can help users get way more out of Twitter. The tools I will share below are only a couple of the many tools users have to choose from. These tools have worked effectively for me on both professional and personal levels.
When it comes to using my iPhone and iPad I use Echofon. Echofon has a free version that has has some ads in it. I decided that since I was going to use Echofon a lot that I would invest $4.99 to get rid of the ads. That was just my choice and it has been worth it. (Thanks for asking.) Pro Tip: purchase Echofon Pro for iPad and use it on your iPhone as well. I haven't had any issues on my phone at all even though I'm using the pro iPad version on it. One of my favorite features in Echofon is the "Mute" feature. I don't necessarily need to unfollow someone or add them to a list when he or she is posting multiple tweets about something I may not be interested in. I simply hit the "Mute" button and do my best to remember to "Unmute" them later. Echofon allows me to easily navigate between my Twitter accounts while giving me full access to my mentions, messages, and lists for each account. It also syncs between mobile devices so I don't see the same tweet twice if I don't want to.
When I'm on a computer my go to tool is TweetDeck. TweetDeck allows me to add from a list of columns which stream live on my machine. Those columns can be one of my Twitter timelines, interactions (mentions and new follows), just mentions or followers by themselves, messages, resources from a Twitter search (for example, a hashtag I'd like to follow during a chat live), lists, tweets, favorites, trends on Twitter (popular hashtags or topics), recent activity from the people I follow, any tweet or message that has been directed toward me from any account I've linked in TweetDeck in one column from one of my multiple accounts, as well as the option to see any tweets that I have scheduled to be posted later. That's a lot of options. Just for a visual, the "Add Column" option pane looks like this:
It's all a little overwhelming at first, but with some experience TweetDeck became an essential part of how I interact (in a efficient way) from any one of my Twitter accounts.
Again, these are just a few of the many options out there. I wanted to share what works for me in hopes the same tools may work well for you. Good luck and have fun!