Yes, you will need domain services to apply NTFS permissions in either scenario so either an accessible Active Directory environment or else to use Azure AD Domain Services. If you have an AD environment on premises already then with the S2S VPN this is your cheapest option.
If you just require a fileshare then go with Azure Files, no need for a VM at all. This will give you a highly available serverless file share. If you need the Azure VM for something else then it may be cheaper to just add a disk to it but if the VM has any issues or requires maintenance then the files hare may go offline.
The benefits of Azure files are more on high availability, scalability (up and down) and the fact it does not need to be maintained beyond permissions really.
Exact pricing will depend on capacity requirements and performance tiers. Don't forget to factor in backup costs also. If you work it out by the GB a managed disk is cheaper in terms of cost but it really depends on the use case to make the right choice.