Six pounds of supercharged boost would be the equivalent of around twelve+ pounds of turbocharged boost. Engine internals should not need work.
The Eaton style supercharger sits on top of the engine requiring more intake work than a centrifugal and I suspect a different hood to allow for the additional height needed to add the supercharger. They also cost more, but do not need the bracketing a centrifugal does. With a centrifugal supercharger you also need an external bypass/blow off valve, and then you really get the sound of boost, but that additional $300 would bring the cost closer to the screw style.
I am not sure there is a screw (Eaton) style that would fit on top of either engine, so that may rule it out, where a centrifugal sits next to the engine, making that choice seem more feasible.
But if it was me, I would just trade the 1.8 in on a 1.4. And rather go through all the bracketing to supercharge a 1.4, just drop it and put in a 2.0t.
The latter would probably require a different hood, also. And a different tranny.
Ball park $ not confirmed by looking so just guesses:
Eaton style = $5000
Vortech style = $3500 + Blow off valve = $300
2.0T = $4500 + F40 tranny = $1500
Laborsmith