Please advise a "Task Manager"

Try teamer.ru. I was quite happy.

Redmine.
A lot of plugins for sharpening any type of methodology, Scrum or Kanban.

Your small team could play in a Scrum / Kanban.
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Here you can find a list of tools with filters.
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Another note on Redmine, ActiveCollab, Basecamp.

More worksection.com/ nice system.

And the stickers by the way is not so bad =))
For myself I use a Google Chrome app ActiveInbox for Gmail and Google Apps
Adds GTD functionality directly into Gmail. Light, not covered with a bunch of redundant, integrated into mail, which is convenient.

Google Tasks and Google Tasks extension for Google Chrome his ilk.

If you have MS Exchange, using Outlook can be quite successfully distribute the tasks. Another option is MS Project. In conjunction with the server and Exchange tasks will automatically appear in the necessary resources.