Wow, first of all, congrats for upgrading from this ancient build... 2010...
I personally would only move what is really, really necessary. I am not sure if it is possible to upgrade directly frorm 1.91+ to 2.06. Maybe someone else can give information on that.
I personally would do a backup of the database and store it away somewhere. I probably would also create a copy of all LS files in your current installation.
Then I would setup a local test installation somewhere and I would use a copy of the old database as database. Then I would try to upgrade. Either direct or in steps.
Then you can see what happens and if something goes wrong you still have your old installation.
Once you feel that the old database runs well with the new installation, you can create your production enviroment.
But if you export as LSA, you should be able also to export and import whole surveys:
www.limesurvey.org/manual/Exporting_a_su...y_archive_.28.lsa.29