What is the best Stand mixer with 350 or more wattage?
Opinion-based questions aren't a good fit, but I can at least give an answer that's a good fit! How about some things you can use to evaluate a stand mixer?
Check the fit between the attachments and the bowl. Does the whisk reach all the way to the bottom? If not, you'll have trouble whipping egg whites as liquid pools up underneath where the whisk can reach. Does the paddle reach all the way out to the sides of the bowl? If not, you'll have trouble creaming and need to stop to scrape the sides of the bowl more often.
As for power, forget about wattage. That just measures power usage. A combination of horsepower (the force the motor is capable of generating) and torque (which is rotational force specifically) tells you about how powerful the mixer is. Some mixers have high horsepower, but generate comparatively low torque due to the design of the transfer gears. You may have to go to the manufacturer's web site for these numbers.
Check the capacity. If you want to make double batches of dough, you'll probably want something 4.5 quarts or larger. Most high-end mixers have a 6 or 7 quart capacity.
Look for a model with a bowl lift versus a tilt head. That makes it easier to use the mixer without worrying about where it sits with relationship to your upper cabinets.
Hope that helps!