bitflipper
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.
WOW talk about covering all the bases, excellent advice bitflipper, clear concise, accurate.
John, if I had a dollar for every time I felt or even heard of somebody never being satisfied with the sound of their own voice it would be l like I hit the Powerball Lottery.
I have a pretty impressive mic cabinet I collected and built over the years, don't want to brag or drop names, but maybe I should trade some of them in for a new car.
And that's something I actually should do while I still can because with today's mic manufacturing DAW technologies, spending a lot of money on anything isn't as important or critical as it used to be.
And I'm familiar with the Avantone, Warm Audio, Audio Technica to name a few and they are as close to being silver bullet mics as any mic can be, but there is no such thing at any price range, you might as well go out and try to catch and find a Unicorn.
Many don't realize what a great mic an SM58 is because they are so common and cheap. But that didn't stop Michael Jackson from recording mega hit albums with one, I had one for 30 years of live shows until upgrading to the Beta 58, and the only reason for that was because the SM 58 was stolen one night. But the only real thing I would consider an upgrade is the Beta is super cardioid, so it's a tad better rejecting leakage and feedback in live situations. Other great mic that are close to silver bullet vocal mics, but they don't work for everybody, and neither does any one particular piece of gear.
I love the CA2A, it's so good and authentic I actually retired my Teletronix LA2A. It's actually quite superior to the original for two main reasons. It's ultimately reliable because it never needs maintenance, and I can run multiple instances, which I could never afford to do.
I actually had 2 of them for a time with the idea of strapping both together across the output buss for stereo, but it was a real pain to get consistent results every time. I felt it was kinda like getting caught in the middle of conversation of a bickering married couple, trying getting 2 vintage analog LA2A's to play nice with each other.

Waves also released an excellent LA2A clone often on sale for $29 (us) which is almost as good as Cakewalk CA2A. They work and sound identical, but being the CA2A can also be used as a ProChannel module is a real game changer.
And the TKO goes to Cakewalk!
And to close, I once was driven crazy trying to get the perfect acoustic guitar sound for a very anal perfectionist client on a particular piece.
After about a week of frustration, I had almost exhausted every possibility I could think of, a student of mine stopped by with a matched pair of Behringer C2 small condenser pencils he just bought for $60 to ask me my opinion of them. Just for the heck out it, I swapped out my extremely lovely Rode NT-5's...….
And guess what happened?
I don't know what your looking for John, but I really like what you did and how it sounded.
And yes of course, as an engineer I would surely mix and adjust it differently the way I (personally) think it should sound, and believe me, the differences would be very subtle, but you might personally think I screwed it up.
Sometimes the only changes needed are in our attitudes and perspectives.
And while I'm a firm believer of being highly critical of myself as I feel you are being here, I fully understand how easy it is to fall into a pattern of never being satisfied, and that can lead to a bad place to be.