Like Sam said, it sounds like a Powerglide 2-speed automatic. That would mean that it probably has a 307 motor and something like a 2.73 gear. None of this is the stuff dreams are made of. It just means that you have a good, solid, dependable means of daily transportation.
Spending $135.88 for the manifold plus gaskets and cost of shipping would be fruitless. The money would be better spent buying your wife a new outfit. Trust me on this.
In the first place, with the possible exception of the headers and duals, you're starting at the wrong end of the car. It needs gears and a posi first and foremost. Go shopping for a 12-bolt differential and driveshaft from another Impala that has the same suspension setup as your car. I think that style was new in '65, so maybe a '65 to '70 would have the same suspension links. Check the recycling yards in your area and look on craigslist.com. Rebuild it with gears in the area of 3.70:1 and install a posi if it doesn't already have one.
Then when it's built, invite a couple of buddies over for beer and weenies to help you pull the old diff out and install the new one.
Drive the car that way while you shop for another motor and transmission to build for it.
That's my best advice.