If you can, buy the new place before selling the old. That way, when you clean out the place (do you have a pickup truck ?) you can also move gradually into the new place. And you can sell the old place empty of all your stuff.
When I retired at 62, we already owned a perfect downsized house with a manageable 1.5 acres, walking distance to excellent Miocene fossil beaches. That place was a wedding gift to my son - just free rent for three years and then it went back to me. My wife also retired and focused on repairs to the old place to the point where it was over-improved, including new decks, new concrete walks, landscaping, refinished 2000 feet of hardwood floors, all new paint, etc., something that is not necessary in today's bubble market. This bubble is so out of control that my daughter has toured 62 houses for sale on the west coast and made offers on 7, the most recent being 105K offer over listing price and the place, one that needed a lot of work, went for 175K over listing price - for all cash. Its crazy out there. Our old house sold the day it was listed and I even accepted a VA loan - the most expensive way for a seller to sell. We were still working on it the day of closing, with the sellers basically telling us we'd already exceeded expectations as they tried to kick me out when finishing the crown molding in the third bathroom.
There has never been a seller's market like this one. Lots of sellers are selling immediately for all cash, as-is and way over list price. The toughest thing you will face is not selling the old house, but buying a new one - unless you want to live where nobody else wants to go.