How to search tweets only with links
To show results only with links, you can add
filter:links in your search query.
Create Twitter lists by topic to narrow down your timeline (especially useful if you follow lots of accounts.
You can follow other public lists too - I will share a collection on my Twitter someday.
Use TweetDeck to get multiple twitter streams simultaneously. Useful if you have spare monitors.
Pro tip: Enhance TweetDeck with Tweeten
If you care, try out BlackMagic. Gives you all kind of insights on every account (i.e. how many interactions on tweets, gives you insights, for example if followers from a project/person are genuine.
Use minimal theme
Use the Chrome Extension below to transfer Twitter into a really clean UI. I personally like it because it just makes your Twitter slick and shows less distracting blocks.
Using Twitter Shortcuts
Shows highlights and dynamic related content while you browse twitter.