They're perfectly interchangeable. Just a matter of context and style. Tutaj is, in theory, the stressed form, but I can't think of a sentence where it couldn't be replaced by tu.
Why not 'tutaj jestem'? It sound awful to me, but I'm noticing all the others have tu/tutaj before the verb
Since the English translation is often different, i previously tried, here I am but no good.
I guess that's really "Tutaj jestem!" or maybe even "Oto jestem!" (that's kinda like 'behold...!')