If you're not doing any form of Project Management currently, you need to figure out a plan or policy first. A tool is not a plan or policy and shouldn't be expected to solve all your problems.
First, define what your goals are. Are you trying to have better reporting? Get costs under control? Figure out who is available when and for how long? Compare your estimates vs your actuals?
Then, figure out information and practices you need to attain your goal. Timetracking can help you track (not manage) costs and compare estimates vs actuals but has little to do with resource planning. Project planning and scheduling is great for rough availability tracking but doesn't tell you how good your estimates are.
Finally, start collecting the information for one project/group. Figure out what does/doesn't work for them, adjust, and then expand to other projects/groups using the lessons and practices learned.. If you roll it our organization wide on the first shot, no one will know how to use it or what sorts of information needs to be captured.
I used to be a contributor to dotProject - look me up, I'm caseydk - and was one of the group that split into web2project a couple years back. If you're seriously considering dotProject, web2project might be a better choice for the security, improved performance, overall cleanliness of the code, and active development. We've already had our 1.0 release (June) and are going for v1.1 this coming week. Depending on when others find this, check out our Release Notes.