Could be a bad WP, or fan clutch. My entire cooling system was replaced last year (radiator, WP, thermostat, coolant temp sensor, fan clutch) because I was having overheating issues.
Since that overhaul, I had the coolant temp sensor go bad on me again, and it was due to the same scenario you're describing, that the coolant gauge would read hot, then go back down to normal immediately.
Just start with a new thermostat, that's where I would check. You shouldn't have ANY coolant around your thermostat housing if it's not cracked and properly sealed. Your water pump does have a bearing inside, so that could be your issue.
Start with the easy stuff first. A thermostat should be under 10 bucks, and a coolant temp sensor is about 25 bucks. When you replace the thermostat, it's a good idea to also replace the large rubber o-ring that seals the thermostat housing together. If you're having seepage, could be a bad o-ring at that housing, or worse...a cracked thermostat housing...they are just plastic, and crack easy if they are overtightened or overheat. They aren't the cheapest piece of plastic either....