The question of music in Ancient Israel is complicated. First, since no transcriptions exist from that time, no one actually knows what it sounded like. Musical historians also debate the identity of biblical instruments (some of which have modern Hebrew meanings that shouldn't be confused with their ancient forms). Nevertheless, here's an attempt at an answer.
Most of what is known about First Temple music derives from biblical references and the Jewish oral tradition. In the Hebrew Bible, for example, when King David installs the ark in Jerusalem (II Sam. 2:6), we are introduced to some of these ancient instruments:
וְדָוִ֣ד ׀ וְכָל־בֵּ֣ית יִשְׂרָאֵ֗ל מְשַֽׂחֲקִים֙ לִפְנֵ֣י ה׳ בְּכֹ֖ל עֲצֵ֣י בְרוֹשִׁ֑ים וּבְכִנֹּר֤וֹת וּבִנְבָלִים֙ וּבְתֻפִּ֔ים וּבִמְנַֽעַנְעִ֖ים וּֽבְצֶלְצֶלִֽים׃
Meanwhile, David and all the House of Israel danced before the LORD to
[the sound of] all kinds of cypress wood [instruments], with lyres,
harps, timbrels, sistrums, and cymbals.
Again, it's important to emphasize that the quote above is a modern English translation (NJPS) of Hebrew instruments. The oral tradition, first collected in the Mishnah (e.g., Arakhin 2:3-6) and later expounded in the Talmud, discusses in detail the musical service conducted in the Temple. In addition to the choral Levite singers, at least twelve instruments were used on a daily basis, consisting of some arrangement of the stringed instruments known as the nevel [a multi-stringed lyre with a deep tone] and kinor [a smaller lyre with fewer strings], and the percussive tziltzelim [a kind of cymbal]; on holidays, two halilim [a kind of reed flute] were also used.
The same oral source (Ar. 2:6) discusses the makeup of the choir:
אֵין פּוֹחֲתִין מִשְּׁנֵים עָשָׂר לְוִיִּם עוֹמְדִים עַל הַדּוּכָן, וּמוֹסִיפִין עַד לְעוֹלָם. אֵין קָטָן נִכְנָס לָעֲזָרָה לַעֲבוֹדָה אֶלָּא בְשָׁעָה שֶׁהַלְוִיִּם עוֹמְדִים בַּשִּׁיר. וְלֹא הָיוּ אוֹמְרִים בְּנֵבֶל וְכִנּוֹר אֶלָּא בַפֶּה, כְּדֵי לִתֵּן תְּבַל בַּנְּעִימָה. רַבִּי אֱלִיעֶזֶר בֶּן יַעֲקֹב אוֹמֵר, אֵין עוֹלִין לַמִּנְיָן, וְאֵין עוֹמְדִים עַל הַדּוּכָן, אֶלָּא בָאָרֶץ הָיוּ עוֹמְדִין, וְרָאשֵׁיהֶן מִבֵּין רַגְלֵי הַלְוִיִּם, וְצוֹעֲרֵי הַלְוִיִּם הָיוּ נִקְרָאִין:
There were never less than twelve levites standing on the platform and
their number could be increased into infinity. No minor could enter
the court of the sanctuary to take part in the service except when the
Levites stood up to sing. Nor did they join in the singing with harp
and lyre, but with the mouth alone, to add flavor to the music.
This source and others signal the voice as being of primary importance to ancient religious Jewish music. These sources do not explicitly state whether the choir of adults was accompanied by instruments while they sang, but the Mishnah does specify the requirement of balancing the number of instruments with the number of singers.
To get a sense of what religious music sung in ancient Israel sounded like, here is the "father" of Jewish musicology, A. Z. Idelsohn's construction of a daily Temple service, based on the Mishnah sources:
After the priests on duty had recited a benediction, the Ten Commandments, the Shema (Deut. 6:4-9), the priestly benediction (Num. 6:22-26) and three other benedictions, they proceeded to the act of the offerings. And after they were through with the arrangement of the sacrifices, one of them sounded the Magrepha [a rake] which was the signal for the priests to enter the Temple to prostrate themselves, whereas for the Levite that sound marked the beginning of the musical performance. Two priests took their stand at the alter immediately and started to blow the trumpets tekia-terua-tekia [various blasts of sound]. After this performance, they approached Ben Arza, the cymbal player, and took their stand beside him, one at his right and the other at his left side. Whereupon, at a given sign with a flag by the superintendent, this Levite sounded his cymbal, and all the Levites began to sing a part of the daily Psalm [dependent on the day, as discussed in the Mishnah, Tamid 7:4]. Whenever they finished a part they stopped, and the priests repeated their blowing of the trumpets and the people present prostrated themselves. The texts sung by the Levites were not Psalms alone, but also portions of the Pentateuch. (from Jewish Music: Its Historical Development)
Scholars infer what parts of what this Levite music sounded like from the Hebrew text of the Psalms, which might show call-and-response forms or refrains, the use of an unclear instrument (such as the alamot in Psalms 46), or the name of a forgotten scale (e.g., the shminit in Psalm 6).
Hope that helps.