I’m thinking two months’ notice.
This is a mistake. Do not make it.
There are exactly two things giving extra notice will do for you: Jack and squat. It is 100% downside, no upside.
If you make this mistake, what you will find is that they will rapidly replace you in their minds. Your opinion regarding any future project (which is all of them) will not be valued because you won’t be there. You will be a ghost in meetings. You won’t be seen as part of the team anymore. They will naturally start thinking of work arounds that don’t involve you. Your last two months will be a death march, at best.
As others have pointed out, they might not even take your offer. At which point you will come to understand how much your generosity is appreciated. Here’s an experiment. Stick your arm in a bowl of water. Remove you arm. Record how much the water level has changed. That is the exact measure of how much they value your extra notice.
And fair is fair. If there were layoffs coming, you would get exactly no notice. Why do you owe them consideration they refuse to extend to you?
Now, you are not a savage. If they truly value your contributions and wish that you stay on for some additional period to ease the transition, then of course you should entertain the offer, as a reasonable person should. Perhaps you stay on at full salary for a time of mutual agreement. Perhaps you could consult with them at a lucrative rate. You’re leaving. You hold all the cards. It is the company’s job to make the counter offer. But get it in writing.