
allererst
very first
Used to strongly emphasize 'first' in order to express that something is absolutely and without any doubt the first in a sequence.
Das war mein allererstes selbstverdientes Geld.
That was my very first money I earned myself.
very first / first of all
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very first
Used to strongly emphasize 'first' in order to express that something is absolutely and without any doubt the first in a sequence.
Das war mein allererstes selbstverdientes Geld.
That was my very first money I earned myself.

first of all
Used as an adverb with the meaning 'first of all' or 'most importantly'; introduces a priority or the most important point.
Allererst möchte ich mich bei Ihnen für die Einladung bedanken.
First of all, I would like to thank you for the invitation.
The prefix 'aller-' is used to intensify 'erst' and means 'the absolute first'. You can also use 'aller-' before other superlatives to intensify them, for example 'der allerbeste Freund' (the very best friend), 'die allerschönste Blume' (the very most beautiful flower).
Das war die allerbeste Pizza, die ich je gegessen habe.
That was the very best pizza I have ever eaten.
'Allererst' can stand as an adjective before a noun or as an adverb at the beginning of a sentence. As an adjective it is declined; as an adverb it remains unchanged.
Das war der allererste Schritt auf dem Mond.
That was the very first step on the moon.
As an adverb, 'allererst' (first of all) is often used at the beginning of a speech, presentation, or email. It signals the most important or first point that will be addressed.
Allererst möchte ich mich für Ihre Aufmerksamkeit bedanken, bevor ich auf die Details eingehe.
First of all, I would like to thank you for your attention before I go into the details.
first / for now
Zunächst names the first step in a sequence without giving it special emphasis. Allererst, by contrast, emphasizes that something is important before all other tasks. Use zunächst for a neutral sequence and allererst when there is a clear highest priority.

Allererst kümmern wir uns um den Verletzten, denn seine Sicherheit hat Vorrang.
First of all, we will take care of the injured person because their safety comes first.
Zunächst sichern wir die Unfallstelle, danach rufen wir Hilfe.
First, we will secure the accident scene, and then we will call for help.