If you suggest relevant tags to choose from the user has easier work and you can also drive the community to use specific term (sort of guided stemming if you know the term). One of the main problems of tagging is that it is comprised of natural language, so users may choose 'run' 'running' 'ran' 'jog' or 'jogging' as their tag and so reduce the efficiency of the tagging mechanism.
I also think that users tend to relate to the same subjects multiple times, so allowing to tag multiple items with the same tag, like in flickr, is very useful and saves time.
If the design makes it obvious that you should tag, like making it a numbered step in the user's vanilla flow of work, then surely users will tag more.
I think the users will do what benefits them, so if you make the benefit from tagging obvious they will tag. Making the benefit from tagging obvious is related to the specific benefit your site will bring, so it is kind of hard to relate to this since I have no idea what the site is about.