My stove was a wreck when I got it - already repainted once over the original and then all rusted up again. Since there was no way I was going to paint another layer over it, I had to strip it down all the way. This required many hours with 3M Paint Stripping discs on my drill, steel wool, etc. Once I got the majority of the paint off, I hit it with a rag and laquer thinner. This took the rest of the paint RIGHT OFF! Try it. On my stove, it's fully double wall and never gets hot enough to cure the paint, so it just dissolves in the thinner.
So, I now had a stove that was bare metal. I then used 4 cans of Stove Brite charcoal color to paint it, two coats over all of it. I did it during the fall, with temps in the 60s/70s, and the paint would dry in a matter of minutes. Very very good results with the Stove Brite.
I wouldn't screw with primer. Just strip it down and use the Stove Brite. I'm not sure Stove Brite even recommends primer, except maybe on really rusty stoves, and then I think they have their own. Not sure about that.