It isn't about the screws, it is about the careful, accurate pre-drilling. If you aren't sure about your pre-drilling, try practicing on scrapwood and test how the screws fit.
How will the screws be used?
If you are planning to use the screws to assemble the jewelry box itself, then consider using clamps and wood glue instead. For most jewelry boxes, the only screws used are for the hardware - hinges, catches, clasps, knobs, supports, chains, etc. (Sometimes screws are used to attach decorative elements, or used as decoration themselves.)
Jewelry box hardware often comes with matching screws. Otherwise, choose small screws, sized appropriately for your box. They are available in a variety of finishes. Bright brass is popular. Countersunk flathead screws or round-head screws are both common, depending on use.