Yes you do have lots of room to improve. That said, you probably will be overwhelmed if you try Project Server out of the gate. I recommend that you use Project 2010 with Manually Scheduled tasks and for the enterprise side start with either SharePoint Project Tasks (provides very simple cataloging of projects) or look at a SharePoint add-in like WorkEngine (emplive.com) for a elegant sync to SharePoint and a template driven way to manage projects with easy data rollup management. If you should need help with a demo you can contact me at firstname.lastname@example.org
PS2010 is a very powerful enterprise tool. Just remember that for every feature you release a substantial change process may be required in the business, depending on the maturity of your companies Project and workforce management.
Make sure you spend the time to gauge this gap and understand the ramifications to the change process. You can stage your PS2010 rollout to allow time for the people and process to adopt and adapt.
In all agreement. I think implementing Project Server should be treated itself as a project. There are certain aspect of the Project Server ( Timesheet, Resource Pool, Calendars etc.) that may not be the right choice for the first phase of adoption. If the idea is to have a common repository for all the project, then you don’t need Project Server. If the idea is to slowly mature the company in Portfolio Management and Enterprise Resource Pooling, Project Server is the option to be rolled out in phases.