Groups are helpful for managing permissions in an easily scalable way, so I would create a group for each team.
Components can be used to auto-assign an issue, so it might seem useful to have your teams listed in the components field, but whether you do that or not, you still need groups for your teams so to can manage permissions quickly. Depending on your team definition, you may need more than one group per team - maybe an admin group and a developer group. How you grant those groups permissions depends a lot on your particular organization. Roles are helpful if your groups do different things in different projects, but if they are the same across projects, you can grant rights directly to the groups and share the permission scheme across all projects for simpler administration.
You cannot assign issues to a group, so if you do put your teams in as the components, you will still only be able to auto-assign the issues to one user as defined in your component settings. Generally it is better practice to identify the major parts of your project and make those the components. Then you choose the component lead for each item. This allows JIRA to assign an issue by having the person creating the issue indicate the part of the project where the work needs to be done. The reporter is not required to decide who will do it.
Finally, as mentioned, you cannot assign to a group, only to specific users. Some teams create a generic use to represent the whole team and make that user account the component lead. That works if your team is watching the Jira dashboard regularly and can see when that user gets new issues or if you set up an email forwarding rule that forwards the notifications from the email address for that user to the whole team. There are plenty of threads in the answers forum on assigning to groups, so read through those for more ideas.
Assigning an issue to the user who clicks Start is an easy post-function you can add to the start transition in your workflow.
You must be a registered user to add a comment. If you've already registered, sign in. Otherwise, register and sign in.