This thread has become rather complicated with a lot of opinions shared (which is a good thing), but I’ll try to simplify for someone getting into the sport.
For finesse trolling (i.e. trolling with one rod in your hand) you’ll want a more sensitive/responsive rod.
For general trolling such as downrigging, boards, dipsys, etc (i.e. in a rod holder) you don’t need the same feel.
Trolling rods come in three different materials.
1. 100% Fiberglass. These rods are generally bulletproof, inexpensive and not terribly sensitive. They work great for a lot of applications, and are generally at the top of the list for downrigging. They also work fine for planer board rods, whether running just braid or weighted lines like leadcore or copper on a board. An example is rods such as Daiwa Wilderness or Shimano TDR.
2. Graphite rods. These rods are the most sensitive and responsive. But they are also very brittle compared to fiberglass. They are best suited as a single rod in your hand (long lining braid or maybe leadcore). They are also lighter in physical weight. An example would be a St. Croix Eyecon rod. DO NOT USE A 100% graphite rod for downrigging or dipsys. You can and will snap them in half. Okuma has a line called Coldwater that are designed for most trolling applications (they seem to be more durable than most graphite rods).
3. Composite Rods. These are a blend of both fiberglass and graphite. They share traits of both materials. They offer more sensitivity and responsiveness than a fiberglass rod, and are more durable than a graphite rod. They work well for many applications, but caution and care must be used if having them as downrigger rods. (Don’t heave on them to pop a release). A lot of guys prefer them for long lining braid behind boards, others use them for almost every application. Examples include Daiwa Heartlands, Shimano Taloras, Jason Mitchell trolling rods, etc.