Hi Jul,
For your forum, I would recommend using Discourse, which you can self-host on a DigitalOcean droplet. The Ghost platform does not have in-built forum functionality. Discourse is very customizable and there really isn’t any other good options in terms of modern forum software, as far as I am aware.
You could put a link to your forum on a page or section of your website that is accessible only to members of your community who are on a paid subscription, if you like.
For your shop, you wouldn’t necessarily need to use Shopify. Gumroad may be a better and less expensive option. You are correct that Ghost does not have in-built store functionality.
If you have any questions I’m happy to chat on Slack.