What size water meter do I need to connect to county water?
So far as I can tell 5/8 is a common meter size for residential water connections in the US. It'll often be connected to a 3/4 inch pipe. It's normal for the meter size to be smaller than the pipe size.
Some utility providers charge a different base rate according to the size/capacity of the meter (or the pressure delivered, in the case of natural gas). If your water utility imposes a higher recurring monthly charge for the larger meter then it would make sense to take the smaller meter -- unless for some reason you'll require unusually high GPM flow (irrigating a very large yard with the culinary water, for example).
The utility should be able to advise how many GPM can be provided/expected with each of the meters; you should be able to produce at least a rough estimate of your GPM needs by summing the bathing and other water uses that might occur simultaneously.