thermostat question

If your engine was running at normal temp reading on the gauge there is no reason to change your thermostat. It is normal for a closed system to fill the bottle after shut-off. The engine temperature peaks after shut-down. There are 3 things likely to cause the bottle to overflow:
The most likely is that it was too full to begin with. The fluid level in the bottle should be left low in order to alolw for expansion after the engine is shut off and the coolant will be returned to the engine as the system cools down.
The second thing to check for is the condition of the coolant. Check it with a hydrometer to verify the level of boil-over protection. After shut-down hot spots within the block and heads develop which can result in steam pockets and coolant temps over 212 deg.
The 3rd thing you need to do is pressure test the cap. You said that you've had the car for several years and it's very possible that the cap has deteriorated and is no longer holding rated pressure.
Whether you use a 160 or 180 thermostat will have no effect on the running temperature of the engine. That number only refers to the opening temp of the thermostat. In cold winter areas the 160 stat allows the heater to be effective sooner.
I live in the inland area of SoCal where 100+ degree days are common and my personal choice is a 190 stat with a bleed hole to ease coolant fill.