Facebook Pages can be set up for selling; Groups cannot. In my experience, most social groups do not welcome sales pitches of any kind, and those that do, limit them. Few people search FB for stuff to buy, either.
FB does offer promotional services … for a fee. To promote a Page, FB posts ads created by the seller. Pricing is determined by the number of desired impressions (“likes”) on the Page.
Individual posts can also be promoted in the same way. Fees are lower (I believe), but are calculated the same as they are for pages.