Architect of Dynamics 365 On cloud

Dear All,

Kindly share the Architecture of D365 for cloud and Domain requirement.

Below points are required for New Environment:

My customer do not have any Active Directory. So, for D365 cloud what are recommendation of MS for it.

Active Directory on cloud or a on-premises. Moreover, If I will go to cloud active directory (Azure Active Directory or O365) so which service for feasible/recommendation on it.

Also share the requirement of ADFS for it on both cases (on cloud AD and on-premises AD)