Magento 2 Check out as legal entity

I am a beginner in Magento, and generally at using any CMS, so maybe some of these may seem obvious to you, but are not obvious at all to me.

What I need to do for my shop is create a system where, at checkout, clients can choose between checking out as an

  • Individual => Normal checkout

  • Legal Entity => Some new fields appear, such as Company Name, CUI, RO

Also, it would be useful to be able to store these for later use as well

Note I do not expect anyone to give me a full working system on a platter. But I would like some info on where to look to learn more about how to do this maybe?