Huh. One-shot recording? Well, I know how difficult singing is at this point, so here goes. I'll change from my normal reviewing style for this as well, it'll be a short one.
Confidence: You should probably work on your confidence. Don't be afraid of the microphone or singing too loudly, it keeps your voice from being strong enough.
Background noise: Try to keep yourself from moving while singing, or sing in a room where there aren't many nearby objects you can hit. Regardless of how good the microphone is, if there are other sounds that it's picking up it'll reduce the quality of the overall recording. More on how to avoid this will come later.
Tuning & Rhythm: Should check those. How to solve this without going to what I'll talk about to fix background noise is simply training your voice, rhythm sense, and tuning sense. Using a keyboard or something as a tuning note is helpful as well.
Fixing background noise, tuning, and rhythm - more artificial method: If you have Audacity or a DAW, try recording multiple takes of specific phrases, then clipping out the best ones and arranging them to form the full piece. This can take awhile - when I was recording for one piece, I spent over 3 hours on about 40 seconds' worth of mere whispering. More than that on tuned lyrics, not counting artificial pitch correction.
Beyond simple recording: If this is an acapella, try doing more than just singing the lead! Record multiple takes of harmony as well - chords, harmonic lines, possibly acapella drums too. :) That would add another layer of depth to the piece and make it much more interesting to listen to.
-RRC-
-SkyeWintrest-