Questions about this
Do I have to buy the next home before I sell this one?
No, and most people should not. Selling first tells you the real number rather than an estimate, and it means you negotiate on the purchase without a contingency. The cost is that you may need somewhere to live for a few weeks. Buying first avoids that and risks carrying two mortgages if the sale is slow.
Is the money left over taxable?
Often none of it is. Under the federal home sale exclusion a single filer can exclude up to $250,000 of gain and a married couple filing jointly up to $500,000, provided the home was your main residence for two of the last five years. Gain is measured against what you paid plus improvements, not against the sale price. Speak to a CPA before assuming.