How to think about Start-up Equity during negotiations?

I wonder if this is a good place for this topic…
I'm in the final moments of negotiating with a start-up for a director position. Comes with options.

I am a little confused about the strike price. In conversation, they said a number, but even though I've asked they haven't put it in writing. The offer is to “upon first day of employment, propose to the board to award X# of common stocks”. The folks that I'm talking to were there before last funding, so maybe their strike price is lower than what I would get. Doesn't that line up?

New to this, but my understanding is that strike prices are usually equal to the FMV of the company's stock on the day the option is granted. This is a pre-IPO company, so private for now. Headed into another funding session.

How far off am I on being concerned? Would a company simply give you $k worth of stock with value above the gift value or is it always you get it at face value and you reap what you sow in the value improvements? I'm under the impression I'll have 300% of the strike cost kind of built-in (obviously with the risk that come with start-ups).

Hit me with your thoughts.