How you choose to store OAuth tokens is up to you, although you do need to keep them private so if you’re running a site, or have an app, you’ll ideally want to have the token stay on your backend rather than on the client.
For notifications, the best way to get follower notifications is to use webhooks, the guide for which can be found here https://dev.twitch.tv/docs/api/webhooks-guide/
If webhooks, aren’t an option in your setup, then you’ll have to poll the follows endpoint https://dev.twitch.tv/docs/api/reference/#get-users-follows
As for subscribers, there’s no webhook or Helix endpoint for that (it is on their roadmap for the 2nd half of this year), so your options are to either poll the v5 endpoint https://dev.twitch.tv/docs/v5/reference/channels/#get-channel-subscribers using a token from the channel you want to get subscribers for and with the channel_subscriptions scope.
Alternatively, you could use Chat or Pubsub if you want real-time notifications for subs.