The tool that suits your requirements is Asana. It promises “teamwork without email.”
Asana has Google Drive integration, the ability to forward an email to Asana, and have it be automatically turned into a task and a comprehensive list of keyboard shortcuts makes Asana a top contender for usability and functionality.
Asana is priced based on the number of users and is actually free for the first 15.
Have a look at this for a summary of the project management tools.
Hope this helps!