I work public sector and gave the head honcho a 30-day notice, beyond the required 2-week notice. Our hiring process, testing, interview, and back ground take months and months. 30-Day notice is plenty for you. They'll live.
"the required 2-week notice" ...
"Our hiring process, testing, interview, and back ground take months and months. "
I ended up starting conversations about 2 months out, and that turned out great. Everyone was very supportive, and multiple leaders in the company have continued to reach out letting me know I'd be welcomed back if I ever decided to unretire.
At my first job we were told how lucky we were to be working at such a desirable place and we should be glad to have been chosen. So after about 5 years I thought I would check out a few other competitors. A couple of years later I had all my ducks in a row and a signed contract with what I (and many others) determined to be a much better work environment with better benefits. It helped to have a background in which it was difficult to find a qualified person. I then announced that I would be leaving my old job in a few days.I would give the amount of leave that you can live with. As in your character can live with. This is really all about what is best for you and it sounds like it is two months. Agree with what someone above said, make sure you have all your ducks in a row because they very well might escort you to the door. I have a specialty occupation and the minimum time I would give would be a month. Best of luck in your new chapter in life.