10k resistors are quite common to use. For example, if I have a count input pin, that is triggered when the pulse is HIGH (1), then there should be a 10k resistor to ground (note that this is unneccisary if you are using the output of another chip to get a signal. Thats because the other chip will allready have the logic at either 1 or 0, not (as its called) floating.) Generally speaking, if the pulse required to trigger something is a 1 (high) then the resistor should be to the ground , and vice-versa.
As to why your counter starts up at 2, Im not 100% sure. I do know, that it shouln't - it should start from 0 (BCD outputs all low). Perhaps stray charges are infiltrating your 'count in' pin, so try the resitors suggested. If that doesnt work, perhaps the power supple, but this seems unlikely (I am assuming you're using a battery? this would eliminate these issues).
Try the methods suggested, then see what happens.