Smaller tires are generally quieter, go for the 16" rims instead of the 18". You'll also see better mileage usually.
Tire thickness is another factor, get the lowest speed rating tires you can if you don't need to go faster than 112 mph/180 km/h, the recommended speed limit of the common rating 'S'.
Of course you should avoid studded tires if you're optimizing for noise, but also All-terrain tires are going to be loud.
2. Smaller rims do not mean smaller tires. On a given car model, the outside diameter of the tire will be essentially fixed. If they have multiple wheel diameters, the tire sidewall height will change to accommodate the wheel diameter. Technically smaller-diameter rims actually mean larger tires.
Tire thickness is another factor, get the lowest speed rating tires you can if you don't need to go faster than 112 mph/180 km/h, the recommended speed limit of the common rating 'S'.
Of course you should avoid studded tires if you're optimizing for noise, but also All-terrain tires are going to be loud.