I use 65 pound brain (but I fish dams with big weights and big catfish.) small cats, and such 10 pound mono. 20 plus pound cats, 50 braid, atleast.

For flathead catfish, some good stuff to use is Stren low visibility 8-12 pound braided line. If you're going catfishing in an area that's known to have big flathead catfish, I'd go with 20-30 pound line or greater. The other thing to think about is how open the shoreline is. If there are a lot of logs in the water, you might want to go with thicker fishing line. If the water is clear, use a low visibility line, otherwise catfish will not notice the line as much if the water is muddy!!!

Depends on what you consider large. I like 35 pound with 60lb fluoro leader to handle abrasion. This should handle anything up to 120 pounds or so. I like to have extra line on the spool unless I am around real trash. If they will get in the trash, I would go with 50lb or 65lb. That way, if they get stuck in something, you can hitch your line to a tractor and drag them up.