Will cast bullets work in a AK-47?  If so, any recommendations as to the exact bullet to use?

Cast bullets can work, but you usually need to use gas checks.

Since high power rifles drive the bullet at higher velocities, unless you load way down the bullets will lead the bore badly.
This often means the rifle will not function in semi-auto.
You can buy gas checks, which are a metal "cap" that fits over the rear of the bullet and allows shooting higher velocity lead bullets.
This requires a special swagging device to crimp the gas checks on the bullets.

Here's some basic info on gas checks and lead bullets:

http://en.wikipedia.org/wiki/Gas_check