I would make a disk image of the current install.
You can make an image via disk utility.. but I recommend you download and install Carbon Copy Cloner.. and create a bootable clone. CCC is free to use for a month.. and IMHO it is well worth the license fee.. but that is not needed just for a clone.
It should be possible to boot the new laptop from the old install if the computers are not too many years apart. You can install an update over the top of existing install and get it working without destroying your user files.
I will need to check if such things are still true for Sierra though.
Certainly it can be helpful to store your keychain.. as keeping track of all the passwords can be a total pain.
To some extent it will also depend on browser. One nice thing about chrome is that you actually sign into the browser not just the OS.. and google keep a copy of your settings and favourites etc online.. It can make swapping computers really easy. Not sure what safari offers.. but you should be able to export a lot of the settings.
While saying nice things about chrome my latest computer problems seem to have corrupted chrome in some way so the world is not all roses!!