Shop vacs make a lot of noise: 85 decibels and up is typical of unmuffled units, 60 db for those with mufflers. Decibel levels above 80 require ear protection. (Always wear ear protection when the vac is connected to a power tool.) An add-on muffler (about $10) quiets most vacs to acceptable levels.
An internal switch should automatically shut off the vac when the tank is full.
Bigger might seem better, until you have to empty it when it's full of water. A 10- or 12-gallon capacity is the most practical for household use. Plastic is lighter and cheaper than stainless steel, but steel is more durable. Tall vacs can tip easily. Low units are more stable, but this limits capacity. Try pulling the vac by the hose — if it tips, don't buy it.
Saves the trouble of grappling with a water-filled tank to empty it.
Four wheels are better than three, and at least the front two should swivel. Outrigger wheels improve stability but require a wider path and are more likely to get tangled.