Synq- The problem is the question is very general, and the answer has many possibilities.
First is the problem of actually making the board - there are guidelines for the minimum drill size that the board manufacturer is able to use for a particular board thickness. The hole has to be drilled oversize to allow for plating the hole, and the oversize drill can't wipe out the copper annulus - that determines the minimum pad diameter before plating. The density of traces and other pads also places a practical layout size constraint for ensuring clean etching between board features.
Next is the electrical concern for the via. How much current will it have to carry? High current requires multiple vias and/or larger barrel diameter.
Signal integrity requires examining via characteristics for fast risetime signals and high frequency signals. Vias have both inductance and capacitance. The designer has to analyze those parameters if the signal cannot tolerate the distortion/reflection/attenuation/coupling that will be caused by the introduction of via inductance and capacitance.
The short answer is that you can use any convenient via size that meets manufacturing limitations for non-critical signal paths. If you are talking about fast, high frequency, signals - you need to do some engineering, and analyze the impedance and coupling characteristics of vias with respect to their surroundings on the board.