In Italian, many adjectives can come after the noun, but some commonly appear before it, especially when they express broad, descriptive ideas like whole, entire, certain, some, etc.
So l'intera raccolta sounds natural and standard.
If you put it after the noun:
it is possible, but it can sound a bit less natural in many contexts or more emphatic/stylistic.
Because nel is the contracted form of in + il.
Italian often combines prepositions with definite articles:
So:
Because in Italian, it is very normal to use a definite article in expressions like this.
Even though English often says simply in cloud storage or in the cloud, Italian commonly treats cloud as a noun with an article in this structure.
So nel cloud is the standard way to say it here.
Usually, for this meaning, nel cloud is the natural choice.
In cloud can appear in technical or business language, but often more like an adjective or label, for example:
So in your sentence, nel cloud is the best option.