I just signed an offer for a new position I am supposed to start on November 30th. I was thinking about giving in my two week notice on Friday, November 6. However, would it be much better to tell them this coming Monday, November 2, to give them a bit more time? Or should I just wait until Friday?
This depends on your relationship with the company. Obviously it's better for them the earlier they know. But it's usually better for you the later they know.
Once you have given notice, your status changes, you essentially go in to a holding pattern, and many employers will now take as much advantage as they can to get you to do extra training, documentation etc,. in preparation for you leaving. While you will be more focused on getting out. At the end of the day the companies needs and yours are now different and I find it's best to make that period as short as possible.
So my advice would be wait and give them 2 weeks as per contract.
It is better for the company if you tell them sooner rather than later. Whether they will respond in a way that is also beneficial to you is something we can not say. You will have to decide if there is the potential for negative consequences to yourself if you tell them earlier, and if so how much you are willing to risk for their benefit.
Note that there are potential benefits to yourself of informing them earlier, and even potentially to a negative resoponse from them.