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Unless your using a special process via plating thickness is generally half your board copper thickness, e.g. a 1 Oz board begins as a 0.5 Oz board, they then put it through some chemical baths so the copper can plate to the via hole walls, then plate the entire thing with another 0.5 Oz of copper, making a 1 Oz board with 0.5 Oz via thickness
Because Via's are plated on in an electroplating bath your minimum hole size is determined by the board thickness, you generally don't want your holes smaller than 1/8th of the boards thickness, as the plating solution will struggle to make it down to the center of the hole, where this happens you can have the plating plug on one or both sides and leave a void in the center of the hole.
1/4th board thickness is for high reliability stuff, the chance of a hole voiding with that aspect ratio is almost 0, 
because they are formed by a plating process, there thickness is not uniform, in general they will be thicker towards the edges, and thinner towards the middle. a 1/4 hole will be highly uniform, a 1/8 much less so, 
If you do want to impedance control your via's focus more on how far you pull back your ground planes from the pads, and place return path vias spaced correctly to define it,