I have to use via to route small analog signals. If I want to minimize the effect of via on the signal, should I increase the annular ring size or hole size. Lets say the total via diameter is same in both cases.
Since you're dealing with low frequency (DC-audio) low level signals, you don't need to worry at all about the vias. Just pick a size that is not right up against the limits of what your PCB maker can handle so the connections are reliable, and leave extra clearance beyond the minimum.
The main layout worries with low frequency uV signals are thermoelectric voltages (if you need DC precision) and RF pickup (minimize loop size and keep things symmetric where that makes sense).