Cheap weapons are going to give you the same problems, no matter what the weapon may be.
Cheap nunchaku (25 dollar range) might not be well-balanced, and the wood they use will not be a durable one at all. Most of the time, you'll get a highly porous type of red oak (not the good kind of red oak) that will often be finished with wood putty, and covered with varnish / paint.
Learning on a pair like these can teach you terrible technique, and most likely, you'll simply end up throwing them away.
If you're dead set on getting a pair, then you may as well get something that you know will not be a limiting factor. Pam over at Crane Mountain, sells some very nice ones, custom made to your specs, and at a reasonable price:
Nunchaku
They do a great job, and have polished brass inserts that minimize cord wear. You can get a pair made out of hickory at a reasonable price (best to call and ask).
Above all, though, try to get some sort of formalized training with them, even if it means traveling a reasonable distance even for a seminar or two. It's actually more difficult to unlearn flawed mechanics, than it is to learn good ones from the start.