Question About Taxes on Gains on Sale of Home

I recently became engaged, and my fiancé brought up that we probably need to get a new house together as both of our individual homes (we're both homeowners independently) are not suitable for our combined needs.

Both of us have around $110k each in equity on our homes. My understanding is that we can each exclude $250k in gains on the sale of a home before incurring any additional taxes. Is this correct? Are there any other tax considerations I need to consider? Does anything change if the new home we buy is in a different tax year than the sale of either/both homes?