I'm thinking of upgrading to a 200 amp service
If you are in the USA, the National Electrical Code is used in most areas as the standard for electrical installations. The NEC requires a minimum of 100 amps for a dwelling service.

From there, it only goes higher with the default for most medium to large homes being 200 amps. Without doing a full load calculation most homeowners choose the 200 amp panel that will be almost the same price as a 125 to 175 amp panel.

In most areas, the utility is responsible for the wire to the service drop, or meter socket if it is underground, but the homeowner is responsible for the meter socket on into the house. So, if they decide to upgrade their wiring it is up to the utility. In my area, the utility provides meter sockets for free but the homeowner or contractor must install it. 

Good luck!