What does 'cheapest' mean in the Ancient Technology rule?
The "cheapest Technology Tile" is counted according to the technology's base price; technology discounts are irrelevant.   Ergo, of all the available technology tiles, you pick the one (that you don't already have) that is left-most on the track.

If there's more than one "cheapest" technology available (i.e. multiple technologies in the left-most column), you can take your pick of them.