I have to create checklist (I am thinking on using tasks list to create a checklist). Tasks will be assigned to different users. Is there a way for each user to track their progress and somehow store their progress in sharepoint.
Yes, you can very well use the task list in sharepoint to track the progress of individual's tasks.
You can create different views by adding dynamic filters like
Me, so that users can track the progress of their own tasks(created by user or assigned to user).
A task list would do just fine for your needs. There are even ways to customize these taskers that have been shown in this group. Just make sure that everyone who can edit their own record has the same level of permissions.