Your intention is to announce the song that you will sing immediately following the announcement.
The choices you've offered for the announcement are:
- Now, I'll be singing XXX.
- Now, I'll sing XXX.
- Now, I'm singing XXX.
The first two expressions are fine. "I'll" means "I will" or "I shall", which indicates a future action.
I shall; I will
"Now" has just enough latitude in its semantic range to mean next in your context:
1.1 At the time directly following the present moment; immediately.
‘if we leave now we can be home by ten’
The third statement would be fine if instead of simply speaking that statement, you sang it. Otherwise, it doesn't sound as fluent as the other two choices.