We really didn't understand this rule (page 7 of the manual): "3 x Ancient Technology: you may take the cheapest Technology Tile you don't already have...". How do you decide what is the cheapest?
1 Answer
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.