You are off to a good start.
Don't polish any greater that 240 or so and probably not even that much. The standard commercial gun polish for a blued rifle is only 240.
You will find paint will not stick the barrel very will even at 240. If you are going to paint it, do about 180 grit, then prime with a good primer and then paint. If you want shiny, paint it with gloss paint.
Do you have access to a bead blaster, that would work wonders.
Polishing a cannon to 2500, if you even can, is going to result in hideous.
The problem with shiny finish is they tend to show the imperfections. Here is the first cannon I ever made. I started on this on my lathe, the day I got home from my very first machine tool operation class in college. You can see the novice operator tool marks in the barrel quite clearly. The gloss paint makes the imperfections stand out. If I had painted the barrel matte the marks would be barely noticeable.
Just something for you to think about.