what is the best type of paint to use?

powdercoat

The paint that's on there, scuffed up a little, and primered over with... something cheap. And a cheap topcoat. But leave the original paint because they used better primer than you have access to.

Or give up on DIY and just get it powdercoated.

You won't actually need to really spray a layer of primer if you just scuff up the original paint... primer is only really necessary if you get down to bare metal

self-leveling primer may help smoothen out rough spots (by filling in the scratches) that you've created by sanding the previous paint.

I just finished a lazy version of the steps outlined in this thread: https://www.bikeforums.net/singlespeed-fixed-gear/317072-bfssfg-howto-frame-fork-painting-10-steps-dummies.html

So I used Duplicolor paint. It turned out decent and was a fun summer project.

Duplicolor is soo much easier to use than rustoleum or other "quick-dry" paints.

I really like the Metal Specks paint when it is covered in clear coat.

Worth the extra couple bucks a can. I don't sand the metal specks base. Just layer clear coat on and hit with 1500 grit to smooth, then layer more on, then polish.

nice! good call on the white stripe beside the chromed elements (seat stays, chainstays, fork).

I used the same instructions, but used auto primers that my father inlaw had left over from when he repainted his old Austin Healy.

Glad my technique was tried and true for you. That self-etching stuff makes a world of difference.