If I was handed that vocal track, my first thought would be "good, I don't have to do much to it". It's raw, but it's good.
Of course, you could effect it up but it's not that kind of vocal. Clean and natural is what I'd go for. Which doesn't mean
no digital cheating. Just keep it gentle.
First up, some conservative pitch correction. Not across the board, just in a few places here and there where there are fast pitch changes that fall a little short. When it comes to pitch editing, less is better than more. Make all your corrections by hand, and don't touch any phrase just because it
looks off in the graphic. If you're using Melodyne, also take advantage of its volume editing at this time to lower the loudest words, which will make step two easier.
Next, apply compression. Cakewalk's CA2A is just what the doctor ordered. Don't be afraid to let it do 6-12 dB of compression. You might also consider two-stage compression, with the second stage running as a parallel compressor.
Beyond those two standard actions, it's all a matter of taste, and there are gobs of options to choose from. Double-tracking would be good, especially on the chorus. Mix the double -6 to -12 dB below the main vocal, for subtle thickening. Listen to David Gilmour's vocals on Dark Side of the Moon, which are all double-tracked but you'd never know it.
I would not apply a lot of reverb to this particular vocal, which would make it sound more distant and less intimate. You could, however, automate the reverb to just add a little sparkle to the end of certain phrases.
Another option is delay, again very subtle. If you can hear the delay, there's too much.
Getting a bit further out and a little less natural, consider a very light touch of chorus effect. This can be applied very, very subtly. So much so that nobody would ever guess that's what you're doing.
Another neat trick with vocals is distortion. You want to be conservative, of course, but adding a little grit and/or sheen can be very effective. Even on a soft vocal like this.
Oh, and don't worry about your microphone. It's plenty good enough. I love ribbons, but cheap ones can sound awful and they only worsen over time. If you want to experiment, I'd suggest instead picking up an SM-58 for a hundred bucks, or borrow one to try. Sometimes, a cheap mic is just the ticket - it's about matching the device to the voice. But again, your current mic is fine.