What sort of supercharger?
What you need is probably different to what you want!
What do you expect to get from it power wise?
What is the car going to be used for?
Why supercharger, why not single or twin turbo, hell, why not a built stroker?
Do you have a engineer to sign off on it, engage the engineer first to avoid disappointment, they will tell you what they require, most big shops can point you towards a engineer who will work with them and you to get it sorted
Most importantly, what sort of budget are you looking at?
Paying to engaging a engineer, all the parts required for compliance and building, then the installation and tuning, then getting it signed off all adds up
A well sized turbo build running low boost is probably the cheapest option, a PD and all that entails to get it running efficiently costs alot, and I mean "ALOT" more, a built stroker would cost more than a turbo, but less than a PD done right, but a built stroker is a painless option in relation to legalities
Then, if 4l60e you WILL need to look at getting your auto transmission built to spec, if you don't it will end up with 6 neutrals and a park, if manual you'll need a good clutch/pressure plate or you will cook the clutch
You need to build the drivetrain to match the powertrain
Even on low boost the added torque will lunch some parts of the drivetrain
There is heaps of info on this site about boosted and stroked LS1's, spend the next few months researching and working out your budget