I replied in the other post that you put in Airmdedics thread, I see that you had started this post so you can ignore my other comment.
There is no place that sells a complete kit.
Now as far as the things that you are going to need. As I listed in the previous post in Airmedics thread, look at the sticky on the top of the drivetrain section, go to the clutch thread, this will give our recommendations as far as clutch systems go and the best bang for the buck.
Also are you sure the T56 that you have is rebuilt? Just be cautious of people selling stuff like that, I just did an installation for someone and he was told the same thing, but found out it was a 150K tranny that was on it's way out.
Now since you don't have the flywheel dust cover, F2B makes this and it is a very nice piece
You didn't mention if you have the bellhousing, clutch fork and pivot or anything like that.
The bellhousing is going to be hard to find if you don't have it, look on Ebay and maybe LS1tech for parts.
I will try to give you the best knowledge that I have for the parts that you are going to need for the swap.
What gears are in your diff in your car, factory? You can run this way but it will eat clutches up.
you are going to need to look into gears later down the road if you don't have them already as well as a driveshaft, Denny's takes about 2 weeks to get, and they are the best to get one from.
Hydraulics clutch/ master and all that can be found at RMS auto and any local parts store, look on ls1tech for used ones, etc.
Flywheel you can get new at Advanced Auto for 104 bucks out the door with no core charge.
If you don't have the clutch fork and the necessary hardware for this,
These are the GM part numbers, you will have to google them
fork-12523312
http://www.rmsautoparts.com/proddetail.php?prod=12523312
bolt- 12523314
http://www.rmsautoparts.com/proddetail.php?prod=12523314
t stud/net- 12523313
http://www.rmsautoparts.com/proddetail.php?prod=12523313