Basic climbing disciplines:
Toproping - The rope runs through an anchor at the top of the climb. The anchor may be slings around a tree with carabiners, bolts with rings, trad gear placed, etc. Both ends of the rope are on the ground. The climber climbs while the belayer pulls through slack. The climber can never fall more than a few feet. Objective danger is quite low if the systems are rigged correctly and both people know what they are doing.
Sport Climbing - Both ends of the rope start on the ground. The leader ties in and ascends the rock, placing quickdraws on pre-placed bolts in the rock. Assuming that the route is fairly reasonably bolted, risk is minimal. Falls should never be more than 20 feet or so, and one is virtually assured that the bolts and quickdraws will function perfectly.
Trad Climbing - Both ends of the rope start on the ground. The leader ties in and ascends the rock, placing camming devices, nuts, etc in weaknesses in the rock such as cracks, pockets, etc. The riskiest pursuit of climbing, as gear may fail is placed poorly, or is adequate protection possibilities are not found or utilized properly. There is no assurance that there will be reasonably spaced protection available.
Toproping is of course cheapest, with sport climbing next, then trad climbing. For all three you will need a rope, harnesses, belay devices, and attachment pieces such as slings or a Personal Anchor System. Beyond the cost of basic toproping gear, a set of 12 quickdraws for sport climbing will run you about $100 - $200, depending on the quality purchased. A full trad rack of cams, nuts, etc, will run between $1,000 and $2,500. Gear seems to accumulate. I have forty cams, several sets of nuts, and tons more gear. Between rock climbing and ice climbing, I have more money invested in gear than in my car (and I don't drive a POS).