I did something similar to this recently on a no-name bass that had a truly nasty 'sunburst' thing going on. The main thing I discovered is that for success you need to have an appropriate surface for the new paint to key into. Not being an expert, I would assume that the exact nature of that surface will be determined by the paint that you plan to use?
I just went to a local hardware shop and asked their advice on paint, which they were happy to provide - I had tried to get some paint option input from a well-known DIY chain, but they kind of looked at me blankly, since I wasn't painting a wall. Unfortunately I don't recall exactly what paint I used and have disposed of the evidence, but both undercoat and top coat were from the same manufacturer and it was straight out of an aerosol.
Don’t know if that helps? The other worthwhile bit of experience to pass on would be that this will take time and patience. I spent a weeks’ worth of evenings on the preparation (rubbing down etc. with increasingly fine sandpaper) and probably another week, half an hour or so per day, applying coats of paint so as to allow for drying time. I also stripped the bass down completely at the start to avoid doing complex masking i.e. all hardware out and neck off, which was a pain but worth it in the end IMO.
Good luck though – it is satisfying when done