"For he who sings not only praises, but praises with gladness. Whoever sings praise not only sings, but also loves Him of whom He sings. In praise, there is the speaking forth of one confession [of faith]; in singing, the affection of one loving" St. Augustine of Hippo (354-430). I would add to that, "For he who sings not only praises, but prays. Not only is our singing in a very real sense prayer, but sometimes the texts are specifically prayer." Psalm 59:16 says, "I will sing of Your strength, in the morning I will sing of Your love; for You are my fortress, my refuge in times of troubles."
Not often do I quote Popes, but John Paul XXIII stated, "[Jesus Christ] is the one high priest of the new and eternal covenant, Who by accomplishing our salvation offers perfect worship to the Father." For me, I think one of the highest forms of worship is when song and prayer are combined. We need to do this in our private worship time as well as when we gather as the Body. Because we need not only private prayer but corporate prayer. And then one day we will worship perfectly, combining praise and prayer before the throne.
I know I bring up Col. 3:16 a lot, but again our singing and our praying has to come from scripture getting off the page and into our hearts. When it has become a part of us, it is completely natural for us to sing a Psalm, Hymn, or Song even by our own making to the Savior. We heard today in worship that great old Southern Gospel Song, Oh, What a Savior; what a time of singing and praying and therefore worship.
Especially in your private worship time I would encourage you to sing pure scripture; songs you remember and prayers to God. It will bless you and, more importantly, it will bless God as we worship Him! mjm