For some custom things, like Visualforce pages, you can get away with staying in Lightning; it plays pretty well with Visualforce. However, there's a large laundry list of things not yet available in Lightning Experience (LEX). In those cases, you must switch to Classic in order to see or use the feature. The limitations are outlined here.
You're absolutely right about the mode selection, though. Lightning is a full screen, single page application (SPA), while Classic is generally rendered one page at a time. The two are mostly mutually incompatible, though you'll find some places where Classic was exposed through to Lightning in order to make the feature available in LEX. These pages will become fewer and fewer as salesforce.com continues its march towards a mobile-friendly UI.
If your user needs access to an item mentioned as Classic-only, odds are, they will be required to switch to Classic mode. You can't generally force a Classic page to appear in Lightning at all, even if you try to trick it with a force:redirectToURL or iframe trick, because the Content Security Policy (CSP) of Classic will prohibit it from loading.