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?
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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.
Personally I don't reckon that the cheapest technology discovery tile is really worth taking advantage of and depending on your stage of the game the victory points are probably more valuable to you. Obviously this wouldn't be true if the cheapest tech is still a really advanced one.
One thing to consider when deciding whether to keep a "cheapest technology" though, is whether it also advances your research track sufficiently to start providing solid research discounts, which is a definite boon even if the technology itself isn't very exciting.