When you go on month to month after the end of a lease, the provisions of the last signed lease still apply. If the lease said you need to give 60 days notice, then that's what you do. If it said 30, then you only need to give 30.
Wow a house for Xmas. Your parents want to adopt another kid?

You need to find out when the house will be ready. Then give notice according to the terms of the lease going backward from that date. You might want to give yourself some leeway just in case the house isn't ready or doesn't close in time. lest say its supposed to be ready on Xmas eve, you might give notice that you will move out by 12/31.
You mention this is an apt complex. So it is less likely to pull some of the keeping the deposit tricks smaller landlords are prone to. But you should protect yourself by taking pictures after everything is moved out, or doing a walk thru with the complex mgr or some other third party.