Learn Hardcore Finnish: Me molemmat olemme valmiita nyt.

valmiit is the “textbook” agreement form; it feels a bit more categorical/neutral in standard written Finnish.
valmiita is very common in everyday speech with adjectives that describe a state (ready, tired, etc.). It can sound a touch more colloquial or “state-like.”
In negative sentences here, the partitive is the natural choice: Me emme ole valmiita. Using valmiit in the negative sounds off.

What’s the difference between valmiit/valmiita and valmiina?

valmiit/valmiita (predicate adjective) = “(both of us) are ready.” General readiness as a state or property.
valmiina (essive) = “in a ready state/position,” often with a concrete, situational flavor (on standby, at one’s station).
- Examples:
  - Olemme nyt valmiit/valmiita. = We’re ready now (in general).
  - Olemme nyt valmiina lähtöön. = We’re now in readiness for departure / at the ready to depart.
  - Both patterns with an action are used: Olemme valmiita aloittamaan and Olemme valmiina aloittamaan occur; the former highlights willingness/readiness to do, the latter leans toward being in a “ready state” to begin.

Do I have to say me? Can I drop the pronoun?

You can drop it because the verb form already shows person/number:

Olemme (molemmat) valmiita nyt. You can also keep me for emphasis or clarity:
Me molemmat olemme valmiita nyt.

Is molemmat necessary? Doesn’t me already mean “we”?

Me just means “we” (two or more people). Molemmat explicitly says there are two and that both are included. Use it when you want to stress “both (of us).”

Without it: (Me) olemme valmiita nyt. = We are ready now.
With it: Me molemmat olemme valmiita nyt. = Both of us are ready now.

Where can I put molemmat and nyt? Is word order flexible?

Yes, Finnish word order is flexible and used for emphasis:

Me molemmat olemme nyt valmiita. (neutral)
Me olemme molemmat nyt valmiita. (emphasizes “both” after the verb)
Nyt me molemmat olemme valmiita. (emphasizes the time “now”) All are natural. Avoid tacking molemmat onto the very end; it normally sits with or near the subject or after the verb: Me olemme molemmat …, not “Me olemme valmiita molemmat” in careful style.

Should the adjective agree with the subject? Why not valmis?

Yes, predicate adjectives normally agree with the subject in number (and case):

Singular: Minä olen valmis.
Plural: Me (molemmat) olemme valmiit/valmiita. Using singular valmis with me would be ungrammatical here.

Is there any style difference between Me molemmat olemme valmiit and Me molemmat olemme valmiita?

Slightly:

valmiit = more “textbook/standard,” often preferred in formal writing when the subject is a definite plural (like a personal pronoun).
valmiita = very common in speech; feels a bit more like describing a current, possibly temporary state. Both are accepted in affirmative sentences.

Could I say Kumpikin meistä on valmis nyt instead? What changes?

Yes. Kumpikin = “each (of the two).” It treats the members individually, so the verb and adjective are singular:

Kumpikin meistä on valmis nyt. = Each of us (both) is ready now. Compare:
Me molemmat olemme valmiit/valmiita nyt. (plural viewpoint on the pair)
Kumpikin meistä on valmis nyt. (singular viewpoint on each individual)

How would this sound in spoken colloquial Finnish?

Very commonly:

Me ollaan valmiita nyt. You’ll also hear:
Me kaks ollaan valmiita nyt. (= “we two”) Both are natural in speech; for standard writing, prefer Me (molemmat) olemme valmiit/valmiita nyt.

How do I say “ready to do something” with this pattern?

Use valmis/valmiit/valmiita + -maan/-mään (the MA-infinitive illative), or use valmiina similarly when emphasizing being “in readiness”:

Olemme valmiita aloittamaan. = We are ready to start.
Olemme valmiita lähtemään. = We are ready to leave.
Olemme valmiina aloittamaan/lähtemään. = We are in a ready state to start/leave.

I’ve seen sentences like Nyt on valmista or Kaikki on valmista. Why is that different?

Those are different structures:

Nyt on valmista. = “Now it’s ready / Things are ready.” (impersonal/existential feel; valmista is partitive singular)
Kaikki on valmista. = “Everything is ready.” (kaikki here behaves as a singular mass) In your sentence, the subject is me (molemmat), a personal plural, so you use plural agreement: olemme valmiit/valmiita.