I've noticed when I shut the main water off for the house, there's still water coming in very little though( dribbling). Is this normal?

Sounds like your shut off is not making a complete seal.closure. It isn't normal and may cause you difficulty doing future repair projests. You may need the city to shut you off at their outside shut off to do the replacement.

It is probably a crappy old gate valve. Chances are if the city replaces it with another one, it will do the same in time. Ball valves are much more dependable and easier to use, and since the 70's, as cheap as gate valves. Why anybody still uses gate valves? Beats me.

Are you shutting it off on your valve or the city valve?