We're currently in the middle of a long distance relocation. How we handled this move isn't relevant to your specifics, so I won't go into it. But we've also done two long distance international moves.
My number one recommendation: Get rid of crap. Sell it, give it away, just slim down to the bare minimum and then cut some more. Cheap/old furniture, the odds and ends that build up over the years, none of it is worth the cost of moving.
Once you've slimmed down your possessions, look into something like POD storage containers. You'll need to verify that they can service both ends of the move. But they can store your stuff between moving out and moving into your next place. Most of the bigger moving companies can do this as well (e.g. Allied Van Lines), more expensive but also an option if you want/need something more full service.
With the above planned out, put your old place on the market. You may be able to negotiate a rent-back when you sell. This may or may not be possible, though not necessary.
At the point that your house looks likely to sell (e.g. once contingencies are removed), start looking for a short-term rental in your new location. You aren't unloading all your stuff there, but rather using it as a base to home shop in the new location. An extended stay hotel works, though a VRBO may be better. Either way, you want something furnished. You are living very light in this phase: clothes, toiletries, laptop(s)...only what's necessary. Depending on how long the house hunt takes, you may need to move again in this phase. Get a PO Box in your new location and setup USPS forwarding to it. While this is happening your POD container is sitting somewhere in storage.
Once you close on a new house, move in and have the POD(s) delivered with all your stuff.
The details may change depending how long it takes to sell and buy a house, but that's more or less how I would do it.
