Are there any preferred handler used for each type of probe which kubelet does on the containers running inside a pod?

The kubelet uses handlers implemented by the container for probing.
The Kubernetes documentation on the Pod lifecycle mentions 3 types of handlers viz. ExecAction, TCPSocketAction and HTTPGetAction.
It also mentions 3 types of probes viz. livenessProbe, readinessProbe and startupProbe.

Is there a preferred handler to be used for each type of probe?

Basically i used only two livenessProbe and readinessProbe. Both has different functionality, liveness check the status of container after container creation and readiness check the status of container before container creation.

@tej-singh-rana which handler do you use for implementing the livenessProbe and readinessProbe.
Do you use the HTTPGetAction handler?