A lot of people put aftermarket satnavs in, as the built in one doesn't do post codes, and updating it requires a little bit of effort to get new discs.
Typical mods (depending on the year of the model, if you have the HR model, (the newer one) it'll have 313, and already have a lot of the tweaks installed.
However, typical mods for performance include, airbox mod (improve the air flow), panel filter upgrade, plenum spacer, exhaust (y-pipe, central and back box) and a remap. Frees up 20-25bhp on average, improves torque and general driveability and throttle response. To get much more gets expensive, and FI is better way to go. However those mods alone transforms the performance and drive ability of the car removing some of the limitations in the first 3 gears.
It handles well in my opinion for a heavier car (I mean it's not THAT heavy really not a huge amount more than a Focus), slight understeer, leading to nice controlled rear wheel control from the pedal, if you turn traction control off it's far more responsive round the corners.
Having seen a lot of track and touge crazy Jap videos, they say despite it being heavier than say an s2000 it still holds it's own - but it's not to be compared to an s2000 which is a dedicated sports car, the 350z is a GT. An s2k will be on it's tails in the corners as it can brake later, but on less tight tracks the 350z handles well enough to keep a s2k at bay.