So now check age of tyres,mileage since bought if known,profile of rear tyre. A new tyre has nice rounded shape from centre top towards the sidewall as you view from the back of bike. If bike has been used for high mileage commuting rather than "scratching round the twisties" use you may find a flat section so as the tyre leans over there is a definite "step" which will feel noticeable as you corner.
Next after tyres-how old is the suspension? If Rear shock is original then will be well past its best at 13 years old.
Front suspension-as already suggested think about changing the fork oil to SAE 15.
Check wheel bearings & steering head bearings are functioning correctly. Also rear swing arm pivot bearings.
Fazers in good shape are extremely well handling bikes and should virtually go where you look/think but like everything time takes its toll but you have the makings of a sweet handling bike without too much £ outlay.