If you're looking for a list of the software options out here, this is a fairly exhaustive list: https://www.capterra.com/task-management-software/

Personally I've used Jira, Trello, and Asana:

Jira: The established leader for more technical task management and is used by organizations big and small for agile software development. I would use this software if your work is technical in nature and you are mainly going to have developers, product managers, and/or designers touching these tasks. In my experience, Jira isn't as easy to use for "non-engineering" roles such as marketing, sales etc. and you could have low adoption trying to push this software to those groups.

Trello: Similar to Jira in its usage mainly for development work and not cross-discipline, but this software is a little lighter weight. This is great for smaller companies who have fairly simple projects they want to track across the engineering/product teams.

Asana: This software is a little simpler to understand for non-tech roles. I've used this well to help coordinate projects cross-division (projects that span multiple teams including non-technical teams like marketing, sales, customer support etc.). Great for keeping the team focused across discipline on each task necessary for larger projects.

Hope this is helpful.