Comparison of Project Management Software Many items listed there can be tailored to fit just about anyone's needs. A lot of it is "free" meaning there's no licensing cost. Anything with a "Proprietary" license will cost you, but non-proprietary open source licenses often have no monetary licensing costs.
There are other costs involved, though. There is a whopping amount of support that's needed in terms of setting up a server (or maybe more than one), customizing it for your needs, periodic maintenance and backups. Then you have to show people how to use it. Then you have to document it so that others may be taught how to use it after "you" are gone.
Look at the features:
Scheduling
Issue Tracking
Resource Management
Workflow
Reporting
Some will do budgeting and time tracking.
The software itself is the least of your worries. The time and effort to set it up, manage and maintain the system are far and away the biggest things you'll need to figure out.
If you can do everything you need in something simple, like Excel, go for it. If you've got nothing maybe start there and take good notes about situations you run into where Excel can't do the job. Then if you want to graduate to something else at least you'll have a better idea of what it is you're looking for.