Oh now this is interesting. I've rewritten my stories a number of times. One of which was an actual webnovel work, rewritten still in the same point of view, but with a far better handle of where I wanted the story to go. And another, which might shine more light for you, was a 15 chapter short story, rewritten from third-person POV into 1st person POV.
I think the biggest thing you have to decided is the intent of the story. Do not ever, in my opinion, rewrite a story simply because it is 'old and jaded' and doesn't reflect your new writing skills. You're just wasting your time there, and you will soon get sick of it. You might as well just write a new story, perhaps one that takes inspiration from the old. If you're going to rewrite a story, make sure its so that you can pull out the intent of the work better.
I rewrote my short story into first-person because it became a deeply introspective work, where the character was always thinking about the world and people around her, and herself. It simply seemed more fitting to be in the head of the character at all times, and I'd say it came out rather candidly.
Now, for clear tips that worked for me:
- Read what you have written previously from the point of view of a humble reader and criticize it. See what works and what doesn't. You might need to take notes on parts that are weak, and parts that are just downright terrible. As well, watch the MC and the other characters closely while thinking about what you had in mind for them.
- This is simply so that, when you actually start rewriting, you know your direction better.
- I would say look at reviews but, if you do the step right, you really shouldn't need to. In my experience, reviews tend to bog things down more than help.
- Read what you have written and see what works. AKA, what you'll be keeping or simply improving/expanding upon. After all, for a rewrite, there's gotta be things that hardly need any changes, right?
- The most important chapter you're gonna rewrite is your first. If you're smart about it, you're gonna find new ways to say more with fewer words. If you're smart about it, you're gonna find ways to improve upon the entire book with just the first chapter's rewrite. If you're smart about it, you're gonna say the same thing, but better.
- And that's about all I've got. Everything else I can think of is more instictual.