I would like to own a plantation.  I grew up on one when I was younger. 
You could probably make good money with the crops you could grow, like coffee or tea or sugar cane as well as cotton.
Are plantations usually big? 
Usually and the plantation houses, especially in the South were quite grand and expensive architectural works.
How much do plantations cost? 
I'm not sure of an exact cost, a lot though. Industrial plantations were established to produce a high volume of wood in a short amount of time. You have many options
Are plantations even existing in North America anymore? 
There are a few, but like every economic activity, it has changed over time
It might be best to purchase one outside of America then.
Plantation
A plantation is the large-scale estate meant for farming that specializes in cash crops. The crops that are grown include cotton, 
coffee, tea, cocoa, sugar cane, sisal, oil seeds, oil palms, rubber trees, and fruits. Protectionist policies and natural comparative advantage have sometimes contributed to determining where plantations were located.
A plantation house is the main house of a plantation, often a substantial farmhouse, which often serves as a symbol for the plantation as a whole. Plantation houses in
the case of the South, which grew commodity crops such as cotton, sugar, and coffee. These types of crops were usually grown on plantations that employed a gang system of labor, which was closely monitored and considered more efficient than task-based work by smaller groups.
Fogel wrote that small farms were just as productive as free farms. He said that the large plantation-style slave farms (16+ slaves) were the most efficient, having a Total Factor Productivity ratio (A/A) to be