You mentioned the importance of activity reports in the webcast. Your boss is not the only audience for these reports - your coworkers can benefit and you can, too. These reports can help you better organize your time and help you prepare for performance reviews, resume updates, etc. You're right - first master the basic responsibilities of the job. As you become more familiar with the company and know your routine, offer your help in other areas, especially when you see your boss or coworkers overloaded with projects.
People appreciate new members of the team who have a positive attitude and take initiative.
What should I do about a coworker who's always trying to get the boss' attention - she's really going overboard trying to get recognized and it's not good for the rest of us. Focus on your own actions - don't hold back just because you think someone else is taking center stage. Your boss may be looking for others to take on greater roles in the department. Tap into your network for ideas on how these people build recognition in their own organizations. In addition, having a boss and coworkers who appreciate what you do can help you be more productive, more satisfied, and more motivated to excel at work - and that benefits everyone.