The core tension
Selling first gives you certainty on price and timeline but may leave you scrambling to find your next home, or renting in between. Buying first gives you a smoother move but means carrying two mortgages, or making an offer contingent on your current home selling, which weakens your position in a competitive situation.
Selling contingencies, explained
A home-sale contingency lets your purchase offer depend on successfully selling your current home first. Sellers generally view these offers as less certain than a clean offer, so a contingent offer may need to be priced or structured more competitively to be taken seriously, especially on a desirable property.
Bridge financing and other tools
Bridge loans and home-equity lines against your current home can provide short-term funds to buy before you sell, though they come with their own cost and qualification requirements. This is a lender conversation as much as a real estate one, so loop in a mortgage professional early if this path interests you.
What actually determines the right order
It largely comes down to how competitive your local market is for each side of the transaction, how much financial flexibility you have to carry overlap costs, and how much risk tolerance you have for a temporary move. There's no universally right answer, only the right answer for your specific numbers and timeline.