Sequence and immediacy (od razu, jak tylko, następnie)

Telling a story in order

You already have najpierw (first), potem (then) and wkrótce (soon). The next link in the chain is next, then (the following step)

następnie — next, then — the neutral, slightly written word for the following step.

in the meantime

w międzyczasie — in the meantime — for what happens while something else is going on.

Right now and as soon as

right away, at once

od razu — right away, at once.

as soon as

jak tylko — as soon as — opens a time clause. The verb in that clause is usually PERFECTIVE and, for the future, in the perfective future: jak tylko przyjdziesz, jak tylko dostarczą.

Within, until now, since long ago

within, in the course of (+ Genitive)

w ciągu + Genitive — within, in the course of: w ciągu godziny, w ciągu tygodnia.

until now, so far

do tej pory — until now, so far — normally with a negated or unfinished verb.

for a long time (up to now)

od dawna — for a long time (and still now) — with the PRESENT tense, where English uses the perfect: Znam go od dawna — I have known him for a long time.

long ago

dawno temu — long ago — with the past tense, like rok temu.