The original "CL trainers" that I recall from the late 1940's/early-1950's were like the 'plank' mentioned near the top of this thread. The had a "lifting" airfoil - flat bottom, curved top - thicker at the front and tapered down to a fairly sharp trailing edge. Vertical 1/2" sheet 'slab' fuselage with a tray for the tank and upright engine. Sheet tail surfaces. Rugged construction.
Fairly heavy, and if the elevator angles were not extreme, with relatively "sluggish" response to the handle .Testor's (long vanished from the marketplace) sold the most often seen, as Jim mentioned, in a few different sizes. The #3 was about right for the .29 to .35 engines of the day. Today's engines generally have more power than those, but set a bit richer they do well.
Over-control is the usual problem for new fliers. It doesn't take much, once you've found where 'neutral' (where the model flies level) is. Once you have a comfortable neutral, you can make the model rise gently by raising your arm, and have it descend gradually by lowering your arm. ...Without moving your wrist from the 'neutral' position relative to your arm. As you get more comfortable, you can relax and fly more confidently. It comes quickly...
Control-line has many possibilities once you've mastered confident level flight and gentle 'altitude' changes. There's so much more you can do that you shouldn't ever be stuck with a boring experience flying CL. I'm not bored yet, and have been flying CL for over 60 years... Welcome, or welcome back, whichever works best!