Twitter is great, but expressing yourself in 140 characters isn't easy. Neither is it easy to keep track of all the ideas and resources that spill through your timeline.
A lot of sharing is done off the social network site through other methods.
A dropbox account means that you can share resources, as it is possible to tweet a link to the resources, which others can then copy to their own dropbox account, or download directly.
A blog means that you can express yourself in more than 140 characters when necessary - like I am doing now. Tags in blogs mean that if you have made a point previous on your blog you can find it again and refer someone to the post.
Pinterest is great for categorising and storing images, and images with links to websites. Downloading the button for your browser makes it easier, or in the mobile twitter app you can get the link to the tweet and pin the images in it.
Pocket is a great app/website, it is a 'read later' service, that allows you to bookmark tweets and links in tweets. On the web browser version you can also add tags to make finding links easier.
Feedly is a great app and website for reading blogs. There are so many tweeters now with blogs, and feedly brings the posts directly to you. Sometimes I don't bother with twitter, preferring to read the blog posts. If you do find a good blog post in feedly it also allows you to post to twitter to share.
Other services to consider are evernote and google. They can also be useful for sharing and saving the resources you find. I also like bit.ly as it allows you to create shortened links with a URL you chose.