I don't even need a search. Just give me a "Trending on Twitter" view. Then as I read through it, make the "Follow" button more obvious. As soon as I click "Follow" then sign me up (or get me to log in).

Even when you go to a tweet from an external link when not logged in, 20% of the vertical height is taken up by a big blue "Sign up for Twitter (or log in)" thing.

Just give me the content and lure me into hitting the "Follow" button.