Just because a thermostat is new doesn't mean it works correctly.
I know nobody does it, but the "correct" way of installing a thermostat involves putting it in a pot of boiling water and using a thermometer to make sure it opens when the water temp gets up to whatever temp the thermostat is rated for. It's actually pretty risky not to check, since if you just install a thermostat that won't open and go driving - the engine will overheat rather quick.
If the thermostat is working correctly, then I'd agree it's the temp sending unit. They don't go bad often, but for the price, sure, it's worth throwing a new one at it to be sure. If that's not it, well, keep it as a spare just in case or for troubleshooting later on.
If it's not the thermostat and not the sending unit, it could be the gauge. You might have to take apart the dash and pull out the gauge assembly or at least pull it forward and look behind it to see if anything looks obvious, though gauges can go "bad" and just need to be replaced, but that's less common than even a temp sender.
As for thermostats, the stock Motorcraft 'stat opens at 190*F, most of the aftermarket ones like Stant open at 195 but some are around 192 or even as high as 197-198. It's just a "range" anyway, they don't actually open at that exact, precise temperature.
For the price, the 195 degree Stant Superstat seems like a good buy for the best performance in cold to warm/hot climates. A 180 degree thermostat might be an option if you live in the Southwest or where summers are 110+ degrees. A 160 degree 'stat is way too cold and will just keep the engine from ever gettting to operating temp and so mileage and performance will suffer.
With the 190-198 'stat, the heater should be able to get the interior really hot in winter, even in freezing temps.