I would advise against just blindly pruning topics, you'll be removing a lot of potentially valuable content... Also, the prune tool in the control panel doesn't have an option to differentiate from stickies/announcements vs user topics; unless your announcements are in a private forum (in which case you'd just not select that forum).
Big question, WHY do you have to have your database under 2gb? I don't have any such restrictions with the hosts that I work with...