Thanks for your question.
There is no mention of dancing as a normal form of worship in the Bible. There were celebratory exceptions though where joy and thanksgiving were expressed in dance. Miriam danced after the Egyptians were destroyed in the Red Sea, Exodus 15:20; Jephthah's daughter greeted him with a dance when he returned home victorious, Judges 11:34; David danced before the LORD in 2 Samuel 6:14; Psalm 150:4 indicates that dance is an acceptable form of praise although it is not clear from this Psalm as to whether it fomed an integral part of regular worship. There is no indication, direct or implied, that dance formed any part of New Testament worship.
I have only ever heard the Church of Christ say that musical instruments are forbidden in worship although the Old Order Amish and Mennonites, Plymouth Brethren, and some very conservative Baptist groups I'm told don't use instruments either.
However, the Church of Christ make it a point of doctrine and one fellow from that denomination with whom I spoke consigned all churches which used such instruments to the fires of hell. Such a viewpoint is very extreme!
Of course it is an argument from silence as nowhere in the New Testament are musical instruments forbidden although there is frequent mention of them in the Old Testament in relation to praise and worship. Indeed, in Psalm 33:2,3 for example, the use of instruments is positively commanded. The whole of Psalm 150 is hymn of joy in praise of God on a variety of instruments including cymbals!
The Church of Christ has, from what I have been told, some wonderful four-part harmony a-capella singing in its services but the New Testament is equally silent about that form of worship too. Does that make it wrong?
They also use a tuning fork or pitch pipe to start their singing. It could be argued that a tuning fork or pitch pipe is a form of musical instrument. That seems somewhat inconsistent.
The fact that the New Testament is silent about whether or not to use instruments in worship is not a compelling argument against their use. God was clearly pleased with musical worship involving instruments in the Old Testament. Why would He change His mind about that?
Apparently God hasn't changed His mind because, although there is no explicit approval of musical instruments (just as there is no explicit approval of four-part harmony or tuning forks), there is implicit approval. It is found in one of the key verses usually cited to support the case for a "no instruments" policy. Colossians 3:16 "teaching and admonishing one another in psalms and hymns and spiritual songs, singing with grace in your hearts to the Lord."
The Greek word "psalmos," means "a song of praise (on an instrument)."
E.W. Bullinger in his critical lexicon and concordance comments on the word as follows: "a touching, twang, e.g. of a bowstring; of stringed instruments, a playing, music; in later usage, a song as accompanied by stringed instruments. . ."
The very meaning of the word "psalm" in Col. 3:16 is a complete refutation of the "no musical instrument" position. "Psalmos" is also used in Eph. 5:19 and 1 Cor. 14:26. The psalms to which Paul refers are from the Hebrew Old Testament book of Psalms. The meaning of the Hebrew word for Psalm, like its New Testament counterpart is, according to Strong's Dictionary of Old Testament Words means, "properly, instrumental music; by implication a poem set to notes."
Frankly, I don't understand what all the fuss is about on this issue. If a group doesn't want to use instruments in their worship, that's their choice and it isn't wrong. If on the other hand they do wish to use instruments in their worship and praise, that is also a valid choice and, indeed, the choice with more solid scriptural precedent behind it.
I hope you have found this helpful.