I belong to a Pentcostal church and attend a Messianic Synagogue on Friday nights. The music in the church is generally contemporary, with some hymns. The music at the syangogue is broken into 2 sections: praise music, which is generally lively, and worship music, which is contemplative (my term). For a sample of the Messianic music, look up Paul Wilbur. The church that I used to belong to only used music out of a hymnal, which I did not find inspirational.
A favorite contemporary song of mine is "Come, Now Is the Time to Worship" by Brian Doerksen. One of my favorite Messianic songs is "In Your Presence" by Paul Wilbur.