My answer depends on an assumption
The term "Mario-like game" means a game like one of the Super Mario Bros. series (SMB). If you meant games like Super Mario 64 or Super Mario Galaxy the answer may doesn't fit your needs but still can be helpful.
You can use both but I would choose the KinematicBody.
At the end it depends on your implementation details. I can totally recommend to read a lot of articles about the physics system and used programming tweaks in the Mario games. You will see that it is often a mixture of approximated physically based computation and well defined edge cases where the calculation results are anticipated, rounded or replaced by a kind of state pattern.
Look into the provided Godot demos. There are platformer (2D and 3D) demos that you can investigate. Also you should experiment with the PhysicsBodies in Godot until you have a good grasp of all the available kinematic methods, collision detection, rigidbody modes and the connection between velocity, acceleration and inertia.
What is the difference between Kinematic and RigidBody?
Answer: Applied mechanics.
You can move your KinematicBody without ever thinking about its mass, inertia, acting forces, friction and damping. But you can also implement parts of a physics system into your movement algorithms (mostly done with acceleration for walking speed and gravity while jumping). So it is sometimes easier to have a very restricted physics environment (KinematicBody) than thinking about every aspect of a realistic behaviour (RigidBody). Some things can be implemented without using physics at all: think about rolling - you can rotate your characters PhysicsBody (torsional moment for RigidBody) or just play a rotating sprite animation.
If you want to read more about the difference I can recommend you these pages (combined with studying engineering mechanics :D ):
If you feel confident with using forces to move your character then try to use a RigidBody. It makes some things easier as it provides a simple interface to a full blown realistic physics environment. But pay attention: The Mario-like games aren't realistic! For example the gravity changes while jumping to make the movement smooth and more reactive. You can also change your direction while in mid-air. These things are getting tricky to implement with a RigidBody.
So in the long run choosing a KinematicBody may be the better choice but you have to implement some physics stuff yourself. :\
Watch videos / Read a lot
But wait! There is more in a Mario-like game than simple walking and jumping. To get an overview you can watch one of these related videos:
You can get an idea of how to implement such things while watching these videos:
You should also read a lot what others have said:
And if you are crazy enough you can jump into someones source:
We are talking Godot here!
Sorry for the Unity, Love2D, LibGDX stuff... I am sure an implementation combined with a tutorial for Godot will be available in the future. There are some attempts here:
[!] Pay attention: None of these repositories seem to have a licence specified.
SMB (and other Mario-like) games are polished like a diamond when it comes to game mechanics and character control in particular. This needs a lot of design thinking (how it should look), level preparation (measurements) and a lot of trial and error (to determine game constants like gravity). Start with a simple platformer with walking and jumping, collision detection and then try to figure out how controlling your character should feel. The decision for one specific node can not replace this experimentation.