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Theres good and bad with each of those 3 choices. First the good.
Turbo: A turbo makes "free horsepower" by using the exhast gases created by the car to spin a compressor wheel which in turn force feeds the engine. There is no parasitic loss from the engine.
Supercharger: Although the power isn't "free", A supercharger run off the engine by means of a belt or gear drive,(note: I'm an older cuss and have seen gear driven blowers. I don't think that you can get one anymore for anything LOL). You will lose some power to parasitic loss, but you won't have the heat that a turbo creates.
Nitrous: Another source of free HP. It can be added to a stock engine, all the way to a full race engine. It can also the finely tuned, regulated, even shut off for street use.
Now the bad.
Turbo: First of all there is turbo lag. Almost all turbos will lag, unless there is a anti lag circut with the turbo. The other problem is heat. Turbos make gobs of heat that can be detrimental to performance. Lastly, you have to run an oil line to the turbo and make sure it's getting lubed. The last one is a minor thing, but lose lubercation and kiss the engine goodbye.
Supercharging: As stated before, there is a small matter of parasitic loss on the engine from the blower drive. as I said it's a small matter on that reguard. There is also a small lag issue depending on what kind of blower you run. A centrifigal blower will have a little lag, where a roots style blower will have none.
Nitrous: The biggest problem with nitrous is more user error that a defect in the product it's self. On a stock engine you can only go so far with the bottle. One step over the line and you will be riding the world fastest handgernade. The other nusence with Nitrous, other than a problen is having to get the bottles filled LOL.
I know I didn't get into comperssion ratios and what octane to run but I hope this gives you a quick idea from both sides of the coin.
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