There are many varieties which have what is called "inhibited suckering", generally when planted the suckers hardly grow at all until the first shoot is done fruiting, and then relatively slowly thereafter. Maoli and Popo'ulu types generally show this type of inhibition, but it also does depend on conditions to an extent. Some common Maoli and Popo'ulu types include: 'Ele'ele, Hua'moa, Popo'ulu and Mai'a Maoli. 'A'ea'e is also relatively common but expensive and more difficult to grow.
Plants to avoid include Namwah, Saba, Kandrian and Orinoco. They are very popular because they are normally rather vigorous, and subsequently make larger "spreading" mats.
That being said, very few bananas really "spread" in the same sense as a spreading bamboo would for example. If your parents have something like spreading bamboos in mind, no edible banana will behave like that (though there are some ornamental/wild bananas which do). They form mats of many shoots, but depending on the variety and location, even if left unpruned they won't necessarily get out of hand.
You may want to consider contacting Going Bananas nursery in Homestead, FL (
Welcome to Going Bananas of Homestead, Florida!). They have all of the (many) varieties they sell growing in the ground and can make a good recommendation for the exact type of plant you are looking for for your situation.