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I won't go into detail, but there is a rod/bait combo that gets you a moat carp 7/10 times at the very worst.
The secret is the bait -- insect paste. The ONLY fish it can target is fish of the carp family AFAIK, so all you need to do is fish in a spot where there's only moat carp, and nothing like tricolored or gold carp (Knightwell in West Ronfaure comes to mind). Little worms are very similar to insect paste (and probably suitable for the poor beginner, since they're bought cheaply and endlessly from NPCs), but they have the added chance of catching a crayfish instead of a carp.
The rod you use doesn't affect what bites; it just affects how easy the target is to weaken, how much time you are permitted to weaken it, and the likelihood of a successful catch as opposed to a line/rod break. Although, if you're going for moats, you don't want to use any rod designed for "big fish", or else you'll just lose some catches to the "too small for this rod" message. Being that moat carp is such a weak fish, I doubt it can break anything.
Anytime you see "Something caught the hook!!!" with 3 !'s, you know that either it's an unstackable (usually big) fish, or a monster. If you know what kind of fish lives in the area you're fishing in, as well as whether or not the bait you're using can attract it, it's usually simple to discern if you have a monster on the line or not.