It depends on if you are a new climber or someone who already has some experience in climbing.
If you are a new climber, then you will probably be more sore than people who have climbed even a few more times than you. One of the main reasons is because some of the muscles that are sore are actually muscles that most people do not use very often.
Climbing puts your body in positions it normally does not go into in day to day life, and not even in many other sports. It also requires you to use muscles differently to be able to stabilize yourself on the wall and climb your way up.
It is very normally for muscles you have never felt before to feel sore, this includes your forearms, back, shoulders, biceps, legs, and many other smaller muscles. If you are a beginner, you will probably also feel some soreness in some very small muscles that do not get used very often, they are used in climbing!
Once you get past the first few initial climbing sessions, the amount of muscles that become sore lessens, but, this really depends on your climbing intensity. If you always have very intense climbing sessions, you can expect your muscles to be pretty sore. But, as you get used to climbing, the soreness goes away, almost to the point where you are not even sore.
More experienced climbers are able to climb day after day, even, depending on the intensity at which they are climbing. This is because their muscles have gotten used to the tension climbing puts on them, and they have strengthened to the point where the normal climbing sessions do not bother them that much. They would need to have a really intense climbing session for those muscles to get sore.
There is no weight limit to climbing, everyone can climb regardless of their weight. Though, those that are overweight may have a higher risk of injury and should be aware of this and be extra careful.
People who weigh more usually tend to have a more difficult time climbing than those who weight less. This is because they need to hold much of their weight on their hands and fingers, which can be very difficult if their fingers are not strong enough to hold this weight and to perform the moves needed for climbing.
Though weight can make climbing more difficult, it doesn't mean you have to be super skinny. There are many great climbers that are on the heavier side, it just means that your fingers and muscles will have to be very strong to be able to pull your weight.
This is all true not just for those who have a high body fat percentage, it is also true for those with a high level of muscle mass. Bodybuilders, for example, may have a difficult time climbing since they will have to pull their whole weight on the wall, which, depending on the size of the bodybuilder, can be a lot.
Being in shape and having a background in some kind of sport can be a benefit when starting to climb, but, it is not a requirement. Almost anyone, regardless of how fit there are and their weight, can climb.
While you climb, you will probably start to feel muscles that most refer to as "muscles they have never felt before and didn't know existed". This is because climbing utilizes muscles that most people usually do not use that often, at least not in the way climbing uses them. This is especially true for people who do not come from a fitness background of some kind.
Climbing in itself can help you get in shape, but getting in shape also depends on what you do outside the climbing gym or away from the rocks. It has to do with how you treat your body, how often you climb or exercise, if you stretch and work on preventing/treating injuries, and of course on your diet.
Neither are necessarily harder than the other, It depends on the grade of the route you are climbing and your skills as a climber. You could climb a 5A top rope route that would be equally easy as a 5A lead route. You could also climb an 8A top rope route, and it would be just as hard as a lead route.
One element that could make lead climbing harder than top rope is the fact that you have to clip your rope into quickdraws while climbing. To do this, you have to be efficient at clipping, and you have to be efficient at resting, since clipping, although it may take a fraction of a second, can tire the climber out if they are not efficient at clipping or if the route is just very difficult.
On the other hand, many people who top rope and auto belay may find it a little bit tricky to make their way around the rope that is always in front of them, which sometimes could be a hassle, especially if you are on a very difficult route and the rope is in your way, and you have to move it, or yourself, to get to the next hold. This, like with lead climbing, requires technique and skill.
All forms of climbing have their difficulties, there is not necessarily a harder climbing form than another. Many factors come into play with this question, and it depends greatly on the climbers themselves.
Rock climbing is possible in sneakers, and even barefoot for that matter, but it is highly recommended to climb in climbing shoes as they will provide a better base for standing on small climbing holds, and give you better stability and grip on the wall.
Sneaker tend to have very soft rubber for their sole, and a generally inefficient shape and size when it comes to climbing. Due to this, trying to stand on small foot holds may be impossible since sneakers have such a large and soft sole, your feet would just slide right off of them.
Climbing shoes on the other hand have much harder rubber, the shoes are much tighter, and they are much less bulky. They are very thin in comparison to sneakers. All of these attributes, plus their shape, give climbers the best performance possible when it comes to feet work.
In climbing shoes, you can actually feel what you are standing on, this allows you to trust your feet much more than sneakers, which is something that for many is very difficult, but crucial.
While a chalk bag is not a requirement for bouldering or climbing in general, it is highly recommended to use chalk as it can be the difference between sending a route and falling. Chalk, when used, is preferably kept in a chalk bag or a chalk bucket, which is similar to a chalk bag, just larger and usually with more pockets for brushes and other items.
Chalk can be essential for those who sweat from their palms, or that climb with others who sweat, since they may be causing the climbing holds to be more slippery for you as well as for them.
Many people also don't think that they sweat from their palms and that they do not need chalk, but, most don't realize that they sweat even slightly, and that small amount of sweat could be what causes you to slip from a hold and not send the route.