Those terms "small," "medium," and "large" obviously don't mean anything out of context. The answer to the general question of rigging thread sizes really depends on (a) the scale of the model, and (b) how serious you want to get about research.
Books are available that will tell you the circumference of every line in the ship. (To get the diameter, divide that figure by pi - or, to make life simpler, by 3. Then divide by the scale of the model.) The best contemporary source for that information is David Steel's
Elements of Mastmaking, Sailmaking, Rigging, and Seamanship, published (if I remember correctly) in 1797. Fairly reasonably-priced reprints are available. The best modern source (which digests all the contemporary ones into a form that's relatively easy to read) is James Lees's
The Masting and Rigging of English Ships of War. (American and British practice didn't differ much, if at all, in the late nineteenth and early twentieth centuries.) Either of those sources will tell you how to determine the precise size of every line - and rigging a model of a frigate to scale will require several dozen sizes.
For a simpler existence, I'd suggest settling on three five different diameters of each color (black for the standing rigging, light brown for the running rigging). Different modelers have different opinions about what the best rigging material is. My preference is silk, but it's hard to find these days. Others like linen; it's good stuff for larger scales, but almost impossible to find in small diameters.
Model Shipways (via its distributer, ModelExpo) sells a cotton-polyester blend line that, to my eye, looks quite realistic and is easy to work with. It's available in quite a few different diameters, and in "black" and "hemp" colors. I believe ModelExpo is currently conducting a 25% off sale on virtually all its merchandise. That might be a good place to look: www.modelexpo-online.com .
One other tip: whatever material you decide on, buy more of it than you need. Murphy's Law, Chapt. 456, paragraph 149: The day you run out of a particular size of thread is the same day the dealer runs out of it.
Hope this helps a little. Good luck.