Nothing wrong with low powered Fiats. My old Uno SX (which I lowered and stiffened and put wider profile tyres on) handle beautifully. In fact with only 46BHP at the wheels it put many other more powerful cars to shame on the track!
In your specific quest you need to tread carefully. You say "running super smooth". Any suspension upgrades are going to make for a more stable ride, better handling, cornering etc. but they will come at a loss of a softer and smoother ride.
What one has to do is balance your objectives. Going back a few years Koni, SPAX, SACHS, others did straight replacement adjustable struts/shocks without the need to go for more advanced coil over setups. This is probably where I would start my research. These were easily adjustable via a knob on the top. Open bonnet/boot and twiddle.
They are also usable with existing springs with the need to lower or stiffen. What uprated adjustable shocks give you is more initial inertial stability, lower roll, lift and drive rates. Of course ultimately the final angle of dangle etc. comes down to spring stiffness and rate.
I suggest you just do a little research into general suspension dynamics and the effect of springs and dampers to get an understand/feel as to what changing any component will do to handling and ride.
When it comes to tyres then this is another ball game. Many people have gone for larger wheels and lower profile tyres only to regret the decision. Generally speaking the lower the profile the hasher/firmer the ride becomes. On the other hand lower profile = less sidewall deflection = lest understeer (not always).
One alternative to radical wheel/tyre changes is to stick with the same diameter tyre and go for a slightly wider tyre with same profile or a smaller profile. There are charts on the web that give you combination of tyre width, profile and rolling circumference / MPH deviation. You make the decision as to what is a reasonable match/compromise taking into account speedometer factors.
NOTE! with a wider profile tyre and the same wheel rim offset (ET number) you have to be certain that the inside tyre wall will hot rub the front struts or the rear shocks / trailing arms and also allowing for tyre deflection whilst cornering. Similarly out wheel arch clearance has to be looked at as well, especially on full lock and suspension load/depression.
One last point! I make/made a habbit of not making irreversible changes when modifying a car. Exmaple: some people want more negative camber so the drill out / slot the top strut to hub mounting hole and then often weld a plate in. Other get their cam shafts reprofiled which may also require the cam carrier to be skimmed. Again to put thing back you have to find another original cam carrier. For me changes should "bolt on / bolt off" and original components able to be refitted.
Just my personal thoughts / experience.