Most Japanese websites use default font sets provided on Windows or Mac. The latest ones are Meiryo and Hiragino Kaku Gothic Pro. For older versions such like Windows XP, it is good to add former default fonts MS Gothic(or MS Mincho)/Osaka.
Some old browsers could not understand those font names in English, some others do not recognize the names in Japanese, so it is safe to write both in Japanese and English.
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Meiryo and Hiragino's order is, because Mac users may have Meiryo from MS-Office, and Hiragino is more familiar and matching well on Mac, better by starting Hiragino series.
So the current recommended practice is like this,
Source: http://stackoverflow.com/a/14573813/4335961
Get the details, frameworks, and tools you need to use system fonts for Apple platforms in your apps. These typefaces offer the control and flexibility to optimally display text at a variety of sizes, in many different languages, across multiple interfaces.
SF Pro
This sans-serif typeface is the system font for iOS, macOS, and tvOS, and includes a rounded variant. It provides a consistent, legible, and friendly typographic voice.
SF Compact
This sans-serif typeface is the system font for watchOS, and includes a rounded variant. It suits a wide range of content and is easily legible in a variety of contexts.
SF Mono
This monospaced variant of San Francisco enables alignment between rows and columns of text, and is used in coding environments like Xcode. It supports Latin, Greek, and Cyrillic scripts and contains six weights in upright and italic.
New York
This all-new, Apple-designed serif typeface is based on essential aspects of historical type styles and is designed to work on its own as well as alongside San Francisco.
Human Interface Guidelines
Read the Human Interface Guidelines to learn how to use these fonts in your app on Apple platforms.
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Videos
Gain insight into typographic principles and how they apply to the San Francisco fonts, the result of a deep collaboration between design and engineering teams. This typeface defers to the content it displays to give text unmatched legibility, clarity, and consistency.
Tools and Frameworks
Use the latest frameworks in Xcode to integrate dynamic text handling and typesetting capabilities into your app.
UIKit
UIKit provides custom text management and rendering on iOS, macOS, watchOS, and tvOS.
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AppKit
AppKit provides font selection, text processing, and rendering for macOS.
Core Text
This text engine and API for Apple platforms provides sophisticated text handling and typesetting capabilities for managing adaptive user interfaces.
SF Symbols
SF Symbols provides over 2,400 configurable symbols that integrate seamlessly with San Francisco.
Apple Font Tool Suite
This suite of command-line tools includes an installer package, tutorial, user documentation, and reference.
TrueType and AAT
Get specifications for the TrueType font format and the Apple Advanced Typography (AAT) Font Feature Registry for advanced font rendering.