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'll contraction
I shall; I will
- ODO
"Now" has just enough latitude in its semantic range to mean next in your context:
Now adverb
1.1 At the time directly following the present moment; immediately.
‘if we leave now we can be home by ten’
- ODO
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.