OP whilst the above makes allot of sense in theory, in reality every solution has it's advantages and disadvantages, and in most cases hidden costs.
Based on my experience, I would advise to consider the cost of maintaining/refurbishing a supercharger especially a Rotrex unit as part of your overall cost of supercharging a vehicle. A centrifugal compressor is the most suitable solution for NA engine due to its power delivery, however in the case of Rotrex the units are a one time assembly item. This is to say you couldn't take it apart to change shaft bearings when thing eventually wear out. Based on my research only one company in America and Rotrex themselves can recondition your blower roughly at £1K in the USA and closer to £2K at Rotrex. I have read statements on the Rotrex website for their products stating 60K kilometres life span with various reports online of units lasting half that. I'm not trying to scare you, I'm only highlighting some of the considerations you should take into account and of course do your research on each solution.
Eaton units are arguably more robust, however as previously pointed out, the NA 1.4 may not have the internals to take the extra torque delivery reliably. In which case IF Eaton is the primary choice, perhaps the base vehicle needs to be a Turbo variant.
If you have the ability and
time to engineer/machine all of your mechanical parts, brackets, piping, etc. then it's doable on a fairly tight budget, but of course some trial and error should be factored in. If you don't have either, then you need to have a few thousand to pay the likes of TTS to engineer a solution for you.
As far as superchargers are concerned, arguably the twin screw is the best bet for overall torque and power delivery at low and high rpm, but at a fairly high cost, and finding a small enough unit for a dinky engine may be a challenge as most of those come from the states and are built for large capacity engines. The smallest unit I have seen is 1.3Ltr capacity, which isn't to say its for a 1.3Ltr engine!
Anyway, some food for thought
If you go ahead though, it will be of interest to see how you get on.
Hum