We use Basecamp and Planner for projects we collaborate on.
Internally my team used Pivotal Tracker for a while (they have free nonprofit licenses that churches qualify for) which was great, but we have since found for IT projects using sticky notes and magnets works better for us.
Since we’re going full O365, we are trying to use Planner, but there are still a few oddities as they roll planner into Teams (i.e. Plans in teams don’t show up in planner’s web app or mobile app, because Teams can have multiple plans per group, but planner can only have one plan per group). That alone is frustrating because that means you have to use Teams on a computer to manage projects.
You can still view tasks assigned to you across all plans/teams in the mobile app and web app though.
I mention so much about Planner because the O365 ecosystem is pretty great and I imagine they’ll sort this out fairly soon, and having everything in one place without asking staff to set up another username/password sounds pretty nice.
Until then, I’d vote for Basecamp or Trello.
Once you start looking into gantt charts and critical path analysis you probably also need to start looking into hiring a dedicated project manager. I’ve found the simpler the system, the more likely it is to be adopted.