Surviving inscriptions using the Elder Fuþark are mainly in late Proto-Germanic and Proto-Norse. The Younger Fuþark was mainly used to write Old Norse (and early Icelandic, if you consider it a separate language from Old Norse). The Anglo-Saxon Fuþorc was used to write Old English.
Keep in mind that the distinctions between the various Germanic languages were blurrier and more fluid during this period of history. You can find inscriptions like the Negau Helmet that seemingly blend Old Italic letters with proto-runic forms, and you can also find inscriptions with a mix of Elder and Younger Fuþark runes.
It is okay to just use "th" when writing "futhark" and "futhorc". You do not need to feel compelled to be as insufferably pretentious as I am.