You have a third option:
3) Follow a publish-subscribe pattern.
To implement this you could use an system such as Amazon Simple Notification Service (SNS). First you would need to set up a platform application containing your API key (for Android) or private key and APNS certificate (for iOS).
When a user starts your app for the first time, the app would ask the user to authorise push notifications access, contact your server and send a token (which is used to register an endpoint on the SNS platform application).
This allows you the ability to send push notifications to the app running on the user's device (which can be handled silently, or be displayed as a real time notification that there is new data available).
You can then set up Topics for each team, that a given user can choose to subscribe to. When the user selects a team, the app sends a request to your server to subscribe to the topic, which you forward to AWS using their API. If a user wants to unsubscribe from a topic you once again forward this request to AWS.
This allows you to send updates for each team to the appropriate topic and have this information distributed -only- to users who subscribe, scalably, and in real time. Your server will only need to ping the topic once and AWS will handle delivery to each user.
Of course, you will need to implement logic to handle the notification, subscribe, register etc. but it does allow your users to receive updates in real time.
Reviewing your options:
1) Easiest to implement and probably necessary for new installs who have not yet registered. You will need this either way so I would recommend you implement this method initially. Your servers will be under load proportional to users however so it would be worthwhile to consider option 3) as you scale (and using a HTTP cache such as varnish or squid to minimise compute and database load)
2) It's not necessary to broadcast this information to -all- of your users but it is effectively publish-subscribe with a single topic (all users). It would be more efficient to only notify users that care.
3) This is the most scalable option and has the added advantage of being real-time. You would be able to notify the user of an update even if they are not using your app at the time. Under a publish-subscribe architecture you will we able to notify only the users concerned with your information, and once updated you can set a timeout value that prevents the user updating from your server until XX time. This way if updates are more frequent than your timeout value users will never need to hit your server.