Remove, clean and lube rear brake pedal with waterproof grease. Same with shifter linkage. Remove, clean and lube front brake and clutch levers. Pay attention to the brass bushing in the clutch lever that pushes the plunger.
At some point, you should look at greasing the bushings in the rear suspension relay arm. Lots of info here.
Check u-joint and drive splines for corrosion and lube.
Check that recalls have been performed. 2006 had some electrical grounding issues. Search "spider" for lots of reading.
Check date codes on tires.
Good luck with the bike and welcome to the forum.
Edit: Be aware of rattling noise on the right side. Some early Gen II FJRs had problems with a weak cam chain tensioner (CCT). I would recommend replacing it at some point. Perhaps along with coolant, sparkplugs and throttle body synchronization (TBS)when you do your first valve check. CCT failure could grenade the engine - not common, but there were a few reported instances.