Obviously the logistics for travelling are one thing, but on your side the work you can absolutely start doing now is compartmentalising the personal parts of your house. Have a lockable area (garage, spare room, etc) that you can store personal possessions. Make it so that as many of your things are easy to box up and stash. It will help if the lockable area is somewhere you can naturally use in daily life; e.g., if it's a study, you can have all your papers in there already, electronics, whatever. Have a clear idea of what things you'll leave available for tenants (crockery, staples, in our case kids' toys).
In our case, the pack-up process was non-trivial - hundreds of items of clothing, shoes and so on getting boxed up. I think that's deterred my wife from rushing to consider it again.
Edit: Looked you up - yep, you're in a great spot. What a dream! House swap?! ;)
I've been on a similar lifestyle for about 9 years now, and I don't plan on stopping.
This may sound counter intuitive, but one thing that worked so well for me is to book a place for a shorter period (like a week), and then look for a place to stay longer. I like to feel the place for myself before making a commitment. It's also easier to negotiate a better deal when you meet the owner face to face.
Shipping travel trunks can be annoying most of the time though. Within the same country, it will be cheap and convenient. Across countries, not at all. Even within the Schengen zone, moving a large trunk can get expensive, and unless the place you stay has an elevator, it will be inconvenient as well.
Assuming you lived at your current place for a long time, you might get snail mails often. I'd arrange a way to get them scanned and emailed to me if I were you, or get one of those services and gradually change the mailing address there.
Once I'm there, I usually get to know a few locals there either in a bar/meetup, couch surfing, or more effectively, with Facebook groups or local classified sites. Locals often have very strong opinions in neighborhoods, likely give tips on where to look for a long term stay, etc. Plus you already have a few friends to invite for a dinner, a game night, etc.
If there is a very nice place that suits well listed on booking/Airbnb, I'd just make a reservation for a couple days and negotiate a better deal with the owners later.