What kind of solid often has the highest melting points?
Giant covalent substances tend to have the highest melting points.
Best examples: diamond / graphite, both with melting points exceeding 3000 degrees Centigrade.
Ionic solids also tend to have high melting points, often over 1000 degrees but they vary. Some are low enough to melt in the lab with a Bunsen burner: Lead bromide for example has a melting point of 383 deg C.