The great benefit of Gmail is the use of labels. Every email starts with the inbox label. Then depending on filters that you setup they can have other labels added. Each message/conversation can have multiple labels, as opposed to a folder system where a message/conversation can only be in one folder.
In a small number of cases some emails will end up in spam, though the user has some control over that as well.
Once you no longer want to see a message/conversation on the front page of the system, then archive the email/conversation using the archive button. This action only strips the inbox label from the message. A message will automatically be reloaded into the inbox if a new message is added to the conversation.
A message can be easily found via searching with label:mylabel. plus the usual methods such as from, date, subject, and that it contains specific words. You can also quickly jump to all the messages with a label by clicking on the label in the list of labels on the left side of the screen.
Look at the documentation, and other questions on this site that discuss the use of filers, and multiple inboxes.
Never delete, but label and archive everything.