This isn’t all that uncommon, it’s pretty doable. GM E-Rod LS3 , $9k . 8L90 8 speed automatic, $6k. Vintage Air A/C system , $2k. You might want a beefier axle, and with an 8 speed transmission, you could do whatever you wanted for the rear end ratio, something milder like a 3.08, 3.31, or 3.55 would work fine. You’ll a new radiator, exhaust, mounts, and you’ll want to upgrade the suspension and brakes as well.
For the interior you can do whatever you want a custom interior can run upwards of $20k, but you can get by with half that if your demands aren’t too outrageous, , budget about $1500-$2500 for a nice sound system. And about $4k-$6k for a nice, better than factory-but not concours quality paint job ( + another grand if you’re changing the color).
If the car is in good shape to begin with, you can probably get all this done for around $40k give or take.
You’ll end up with a car that does everything better than the original car, and could probably get around 15-22 MPG, which would be significantly better than stock, and have significantly better performance at the same time.
Edit: If you don’t already have the car, then figure another $15k-$20k for a 1967 Impala in good condition to start out with. So all in you’re probably going to be around $60k-ish.