There is, yet, an additional consideration. The Gemara in Sanhedrin (101a) states that one may not sing verses from the biblical book Shir Ha-Shirim as a song because one is turning holy words into a song. The Ra'avyah extends this to all biblical verses. However, my impression (and I believe I heard this in the name of R. Yoshe Ber Soloveitchik) is that most posekim reject this extension and apply this statement only to Shir Ha-Shirim. It is very easy to take that particular book out of context and use it as a love song. This is obscene and sacrilegious (and I have seen it done, but that is another story). On this, see R. Reuven Margoliyot's Margoliyos Ha-Yam on Sanhedrin 101a.I don't know where he gets the idea that most poskim reject the Ra'avyah's view. In fact, Rashi on the daf holds that the prohibition applies to all of Torah.
The distinction that "Simcha" makes with regard to there being a specific prohibition on turning parts of Shir Hashirim into songs was also made by Rav Moshe ZT"L (Iggeros Moshe Yoreh Deah2:142) where he suggests it as a justification for the common practice of singing pesukim at simchas (which he opposed), but he concludes "v'tzaruch iyun lamekeilim."
Despite this, though, the common practice is to permit the singing of pesukim and most of the music marketed to the Orthodox community does use pesukim as lyrics. I am curious as to sources that explicitly permit this, though, so if anyone has them and could pass them on...
With regard to using pesukim from Shir Hashirim...even though all seem to agree that the Gemara does prohibit this, there are still many Orthodox performers who compose, play, and record songs using texts from Shir Hashirim. Examples of such songs that are frequently played at weddings (or used to be played) include Hashmeini by Shlomo Carlebach, Kol Dodi by D'veykus (or MBD), and Dodi Li.