Green card renew or Apply citizenship?

You are a lawful PERMANENT resident. That status NEVER expires, not even if your Green Card expired many years ago. In order to be hired for a new job, including I-9 purposes, all you need to show is your driver's license and SS card which is what most people use anyway. you NEVER have to show your Green Card to an employer if you don't want to.

The USCIS wants N-400 applicants to have a Green Card that's valid for another 6 months by the time they apply, but they not that strict about it anymore. The entire process takes in almost all cases only 5, not 8 months. The only exception would be if you lived in a very remote area of the country, where the nearest USCIS office is a 3-day hike away and very few Oath Ceremonies are scheduled throughout the year. You know that you live in such an area if your neighbor has sex with his sheep, so Ozark mountains, South Alabama, etc.

Six months remaining on your greencard may be sufficient as this is about how long the citizenship application takes. However, it is safer to renew the greencard first. Your permanent residence status does not expire but if you had no card, you could not take an emergency overseas trip to visit a sick grandmother.

You can travel internationally during the application period if your greencard is valid. You send in a copy with your application, not the actual card.

You do not hand in your greencard until the actual day of the naturalisation ceremony. Immediately after the ceremony you will take your naturalisation certificate and make two copies of it. One is for your records, the other photocopy, original certificate plus two passport photos and the application form will go with you to the post office for expedited processing. All that happens on the same day.

One week later you will take your new US passport plus your original passport off on your travels.