General questions about setting up company projects

I literally just started on this yesterday. we have 7 or so departments and projects within each. Our business is a winery--so departments are Production, Hospitality, Wine Club, PR, Marketing etc. Some assignees cross over to projects in other departments. I want to be able to view these in cards by assignee or department. Not sure how to do this. Does it make sense to have one sheet for entire company? Would love to talk to some one before i get to far into populating this to make sure i have it set up right...haven't even looked at reporting etc yet. Thank you!

Also, if i wanted to set up my own project task list...do i use a different sheet?