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Go the web-sight of your PCB factory and see what they can do. (depends on cost)
A CAD program can do anything but the real question is in the ability of the PCB machines.
You are looking for min drill size, min trace, min rings.
It really comes down to the thickness of your board. You generally want no greater than a 5:1 barrel length:diameter aspect ratio. This means that if you have a 1.6mm (0.062") PCB and your via goes from the top layer to the bottom layer, the diameter should not be less than 1.6/5 = 0.32mm (0.0124") in diameter. Many manufacturing companies can offer better (higher) ratios, but to be on the safe side the 5:1 is usually a safe bet. The smaller the ratio, the more reliable the via will be. Too high and you won't get uniform plating of the hole, and you risk cracking of the inside of the barrel.
There is no standard, really, but there is popular. For example, 16 mils is popular and presents no challenges to the fabricator. You also need to be sure to provide a large enough annular ring around that hole for the fabricator to avoid problems. I think that an 8 mil annular ring would be ok, so the total diameter of the via pad would be 16 + 8 +8 =32 mils. When you do a plated through hole, you should be specific about what your diameter means. You could specify that the diameter is measured after plating, which means that the fabricator would probably choose an 18 mil drill bit, drill the hole and then plate another 1 mil of copper on the wall of the hole for a net diameter of 16 mils. Or you could specify that the fabricator actually drill with a 16 mil bit and allow them to plate the hole down to around 14 mils or so. If you don't give them any details about what your diameter means, they usually assume you want this diameter after plating.
Blind vias are a bit more complex and you should always consult with your fabricator on appropriate sizes.