Welcome to the Team Jim!
In the Impala the SS was a trim option (a body style actually that offered bucket seats and extra shinny bling but no performance), the SS could be ordered with a six cylinder 230 inch cube fire breathing Hi-Thrift motor.
The only exception to this is the COPO 427SS that was and still is one of the rarest cars made. A true SS427 hood goes for over $4,000 on e-bay if you can find one. The SS427 was a 9C1 cop car without a certified speedometer a deluxe bucket seat interior and a 425 horse 427 engine out of a Corvette undered the twin blisters on the hood.
Though the 427 was offered in 1967 as an engine option it was the passenger car 390 horse version. That engine came with a two bolt main block with oval port heads and a hydraulic cam. The 425 horse 427 had domed forged pistons, a forged steel crank, four bolt main block, solid flat tappet cam (L-88), and rectangular port high performance cast iron heads heads (with the L-88 aluminum heads offered as an option).
If you are building one today (a big block car) buy used a 454 four bolt block truck short block (all Gen V and Gen VI blocks are one piece rear main seal and have four bolt bottom ends). You want a short block because you will be throwing the heads and cam in the dumpster (as well as the two barrel TBI induction). Buy oval port after market heads (240 to 270 cc intake runners) an Edelbriock Performer RPM Air Gap intake and a good replacement hydraulic roller cam shaft (all Gen VI blocks where hydraulic roller from the factory; Gen V was a hydraulic flat tappet cam). An 850 cfm Holley carb, a MSD small cap HEI distributor and a couple of 396 decals.
You can run it as is as a 454 but I would rebuild it with a stroker crank and pistons to make it a 496 (every other BBC you see will be this big or bigger). With today's pump gas you need a lot of cubes to justify the added weight of the big block engine. This is because a SBC 400 with a cam and a four barrel will eat a 396's shorts making 50% more power with 230 pounds of cast iron weight lifted off of the nose of the car. With today's pump gas most buy or build themselves a 540 BBC engine; considering it to be a good staring point.
As much as we as hobbiest drool over engines and power; it is far more important to find a good straight relatively rust free body. A refrigerator magnet can be your best friend when shopping (along with a small screw driver to pick at blisters in the finish).