Azure blob storage is a good, inexpensive way to store files in the cloud.

Putting some thought into how you will use this data will save you some money.

Azure offers 3 tiers of blob storage access: Hot, Cold, and Archive. Your choice depends on how frequently you intend to access your data.

It is always free to upload data to Azure storage, but there may be a charge to retrieve data.

Hot storage and Cool storage each offers easy, quick access to your files if you want to read or download them. The difference is the price. There are 2 components of Azure storage pricing: storage and data transfer. Storage is the fee for using space on Azure hard drives. Data Transfer is the fee to access your data (for example, you may want to download a copy of a file or point to an image stored in blob storage). Hot storage has higher storage costs, but lower data access costs than cool storage. So, if you plan to access your data a lot, Hot storage makes more sense; for infrequently accessed data, cool storage is cheaper. 

There is a third Azure Storage tier called "Archive" that is designed for long-term storage data that is accessed very infrequently. Archive tier differs from the other two not only in price - but in how quickly you can access your data. The storage price is much lower, and the access price is much higher than the other two tiers. In addition, it may take hours between the time you request your data and the time you can access your data.

Hot and Cool tiers can be set at the storage account level, but Archive tier can only be set for individual blobs.

If you want to store 5TB data in Azure storage the cost per month (as of July 2018) would be:

Hot tier $104
Cool tier $76
Archive tier $10

The cost to retrieve 1 GB of data with each tier would be

Hot tier $0.00
Cool tier $0.01
Archive tier $0.02

To summarize:

Tier Monthly storage cost, 5TB Access cost / GB
Hot $104 $0.00
Cool $76 $0.01
Archive $10 $0.02

Of course, these prices can change over time. You can view the current prices at https://azure.microsoft.com/en-us/pricing/details/storage/blobs/ 

As you can see, the costs can vary significantly. Your choice depends on how frequently you plan to access your data. If you want to store images to display on your web site, the Hot Tier makes sense. If you want to store customer invoice PDFs and you expect people to only review them every month or two, Cool is probably the best choice. If you want to back up your video files just in case your local drive fails (like I did), Archive is more practical, because I might never retrieve those files.

As Azure evolves, these options become more and more driven by the demands of the customer.