If you ask specifically about storing application logs in kubernetes cluster, there are a few different approaches. First I would recommend you to familiarize with this article in the official kubernetes documentation.

Try to get some knowledge by yourself. Every storage have some pros and cons according to requirement we use them. Visit https://medium.com/volterra-io/kubernetes-storage-performance-comparison-9e993cb27271 and learn more. I will surely somehow help.

As per my experience with the Kubernetes logging, I would suggest you go with EFK stack (Fluentd/flunetbit --> Kafka --> Logstash/flunetd --> Elasticserach --> kibana), this one has initial challenges during setup but once this is up and running, it will be like a super scalable system where you don't need to worry about volume of logs you are shipping.

Another approach you can take is shipping logs directly from fluentd/fluentbit/filebeat to Elasticsearch. The drawback of this approach is if ES has some issue then you may lose your logs.

I hope it helps.