This is often the single biggest strategic decision for anyone both selling and buying, and there's no universally right answer, only the one that fits your specific numbers and risk tolerance.
Selling first is the lower financial-risk path. You know your exact proceeds before shopping for your next home, and you're not carrying two mortgages or relying on bridge financing. The tradeoff is potentially needing temporary housing if your purchase isn't lined up by the time your sale closes, or negotiating a rent-back period with your buyer to bridge the gap.
Buying first gives you more breathing room to find the right next home without a closing deadline pressuring the decision. The tradeoff is financial: you'll likely need bridge financing or the ability to comfortably carry two mortgages for a period, along with the logistics of two simultaneous transactions.
A contingent offer, buying a new home contingent on your current one selling, softens the financial risk of buying first, but weakens your offer's competitiveness in a market where sellers often prefer certainty over contingencies.
The right choice depends on your equity, your comfort with financial risk, and how competitive the market is on both ends of your transaction. This is exactly the kind of decision worth working through directly with an agent coordinating both sides, rather than defaulting to whichever option sounds simpler on paper.