Hello,
The option of a Storage in Azure is perfect, as for the tier, normally to retrieve files and return them to customers you can use COOL without problem. More than the speed of access to the cool and hot files, they differ in the number of times the file is accessed.
Anyway you can also define a life cycle for the files for example according to their creation date starting with Hot, passing through cool and finally if they are not needed except for archive use archive.