I'm about to buy strings and begin playing my acoustic guitar, but I don't know if there are different sizes of strings.
We refer to the different sizes of strings as the "gauge" or "thickness".
You should probably replace your strings with the same gauge strings that are on your guitar already. If you change the gauge of strings, it will change the tension on the neck, and this might require that the instrument be adjusted by a technician--this is called a "setup" and it usually costs extra money.
So take your guitar to a music store. They can tell you what size strings are already on there and suggest a set to replace them with. They can probably teach you how to change them, too, and sell you an inexpensive string winding tool.
Sets of strings, at least in the USA, are referred to by the diameter, in fractions of an English inch, of the highest-pitched string. For instance, we refer to a set of strings as "12s" if the diameter of the highest string is 0.012 inches.
For an acoustic guitar, generally speaking, people would choose a set of 10s, 11s, 12s, or 13s. Most people use 12s or 11s.
Heavier-gauge sets will be brighter and louder, but will also require more force in the fingers to play. Lighter strings will have a more delicate sound and put out less volume, but will be easier to play.
Also, there is the matter of the formulation of the metal alloys in the strings. The most popular style for an acoustic guitar is "phosphor bronze" but there are others. Ask your local music store about the alternatives.
Wheat covers the details, but if I may pull back and generalize, for many things with guitar, there's Light or Thin, there's Heavy and then there is Medium. If you don't know which you need, try Mediums until you develop enough understanding to know what you need.