I did this swap, and it's pretty straight forward.
You can see some of it here:
http://www.cardomain.com/ride/2407208
I used the LS1 wiring harness and had it modified form Speartech. He did a great job- labeled everything and made it very straight forward. I had to add a couple of relays to power the electric fans and AC. My car originally had a mechanical fan so I didn't have any factory wiring to accommodate an electric one.
If you use the 4th gen ls1 compressor in its stock location you will need to notch your 3rd gen cross member to make it fit. Otherwise, you do not need to modify it. You may need to move your factory brake line though.
The oil pan is a tight fit, but it does fit.
When I set up AC on my car, I used a 3rd gen compressor and used the F-body motorsports compressor conversion kit. I didn't like it, so I won't recommend it, but it is one option you can use. (in my case, 1- it was late arriving, 2- the brackets didn't match and I had to modify them to have the holes align, plus radius the sharp cut edges to avoid slicing my hands, 3- the location leaves a long distance for the belt and it flopped around under load. more then my comfort level liked. However, everyone's experience is different. maybe they improved the kit since then, who knows..)
I used the 4th gen radiator and it fit in my car fine. the only modification to the radiator was trimming the round plastic shaft at the bottom of the radiator. otherwise it fit right in in. I used a 1984 L69 radiator cover on top to secure it.
I had no issue with a short shifter. I also used the Hurst billet shifter in the factory console/ bezel. Personally, I don't like the look of 4th gen interior parts in the third gen. the 4th gen lines are all soft/ flowing and the third gen are much more rigid. the 2 styles don't mix well, imo. I'd leave the third gen console in there and use it. your car, your call..
One thing I highly recommend is using the 4th gen gas tank. It is the same shape, bolts right in and has the correct fuel pump/ regulator built in. Use the plastic tank as it has a removable rubber filler neck making installation much easier. it also needs to be trimmed an inch or 2. this, of course, is easy to do. Looks on thirdgen.org for the correct gm part number for the proper fuel gauge resistor so your third gen gas gauge reads properly. there are threads on what is needed and how to fix it.
I attached a few pics for your reference. If you need these in hi res- send me your email.
I also did this swap and had it California certified. It was a PITA!
If you have any questions, post them or pm me. I hope this is helpful.
-Brendon