"Our team" or "My team"?

In your specific case, I would use 'our'. As you stated, it does sound more collegial and inclusive. (And you're copying your teammates on the message.)

Our is appropriate for situations when you are communicating with someone else on the same team/in the same organization, when you want to be inclusive, and when you want to exhibit participatory leadership or don't have an official leadership role.

My is appropriate for situations when you do have an official leadership role, when you're communicating with someone outside your team/organization, when you'll be delegating the work or otherwise won't actually be doing the work yourself, or when you need to put on a show of strength. In spoken conversation, tone of voice can soften the "possessiveness" of my, but of course, written communication doesn't allow that.

Use our so it doesn't come across as tail wagging the dog :)