Here is my issue : I have two different types of accounts (person and business) but I need different information about them.
For example, I need :
for a person account : first name, last name, date of birth, address, etc.
for a business account : address, ID (SIRET number in France), domain of activity, website, etc.
Is it possible to have, when I create a new account, a first field where I choose whether it is a person account or a business account, and then have the corresponding fields appearing ? (I know it is possible in Salesforce)
I believe the correct way to model this in SuiteCRM is to use Accounts module for Businesses, and Contacts module for Persons. You will find this comes with hundreds of advantages.
So let me turn the question around to you: what do you need to do that uses the two kinds together? Maybe it is already possible (for example, both kinds can be easily added to Target Lists for a Campaign).
You can link Contacts to Opportunities (in the subpanel). So you would have to make all contacts-without-account be a part of some phony account (called “Independents” for example) to be able to create the opportunity, which demands an Account as required field. But then you could select the specific Contact that interests you.
As I said, there are many advantages to staying inside the SuiteCRM concepts as much as possible, since as your usage evolves you will find many problems solved and many nice options available because they are part of the default way of working.