Every VM has a durable OS disk. Meaning, it's backed by Azure Storage (whether managed or unmanaged),and will survive reboots, and even deallocation/reallocation of vm's.
The issue is with size: the OS disk will be either 32gb or 127gb, depending on OS.
You can attach additional disks (up to 2 per core), which gives you more durable storage. If you attach an unmanaged disk, you'll only pay for storage used. Or, for simplicity, go for a managed disk: no storage account to manage. But you do pay for the entire volume's worth of storage.
Note: If you use an unmanaged os disk and an unmanaged attached data disk, there would really be no noticeable difference in cost, since you'd only be paying for storage used, across both disks.
You can also use the in-chassis temp disk, which is SSD-based, but it's not durable and you will risk data loss.