We sold and bought a home but reinvested any profits into the new home we bought. Would it be beneficial to upgrade to Premier?

No, I recommend that you start with the Deluxe version to claim your home deductions - new and 'old' ones.  Reinvesting in your new home is really not an investment for tax purposes.  The Premier is designed for investment properties such as rental, stocks, etc.  

Your reinvestment into new home, whether as a larger down payment or paying for improvements, is not allowed as a tax deduction.  You may add improvement (in your own records) to the cost of the home thus reducing any potential profit. Down payment is simply treated as reduction of your home cost - there is no tax consequence for this at all.