Typesetting non-Latin character sets has long been a challenge not only on HTML web pages. The classiscal ASCII character set consists of 128 character codes only of which the first 32 are unprintable control codes. Localized extensions containing 256 character codes are good enough to typeset near related languages, but as a digital document can have one encoding only, mixing alphabets still remains a problem. On scholarly theological websites true type fonts for Ancient Greek and Biblical Hebrew are provided for download pretty frequently. They simply change codes <= 255 to Greek or Hebrew characters. As all major browsers today understand the @font-face rule it would be possible to convert them into web fonts and offer them for download. But licenses usually forbid that. Some of the large font repositories offer such fonts (Google does not!) but without proper licensing information. Besides this the main downside is that coding is font-specific as there is no rule on which code point to place a particular character. This makes design relaunching or publishing in other environments fairly difficult. And finally @font-face slows down loading time.
Without doubt Times New Roman is the most similar to the printed characters in Biblia Hebraica Stuttgartensia. But print and web layouts are not the same, and serifs tend to display badly on screens due to low resolution and low lighting compared to print. This holds especially for Hebrew since its characters appear relatively small in comparison to Latin as lamedh is the only one with cap height. This leeds also to problems with the tiny diacritics as even with a 16 px font size on a large screen it is hard to tell a patah from a tzere in all instances.
There is an browser issue, too. Internet Explorer (V. 10), Chrome (V. 29) and Opera (starting with V. 15 due to its changed rendering engine) do not render the cantillation marks of DejaVu Sans, DejaVu Sans Condensed, and Lucida Sans Unicode correctly.
All Biblical Hebrew font provide bold and, most of them, italic characters. Monospace is not suited for continuous text in Hebrew as it is not in Latin. The small yodh opens an ugly rift.
The by far best legible font is Ezra SIL. It is distributed under a free license but since a copy of the license has to be included with all shipping it is not suitable for @font-face. In my opinion Tahoma, which should be found on all Windows computers today, is a good choice. I find it pretty puzzling that the ordering of the cantillation marks varies. Do we still suffer from this in the Unicode era or have I missed something?