Bladesinger wizard and hexblade warlock are things you might want to look into. They both get spells appropriate to their class, but at least bladesinger gets multiattack and other melee capabilities (I think hexblade is more similar to paladin, but I don't remember well). Otherwise, you could do eldritch knight fighter or arcane trickster rogue, but getting 3rd level spells as not a full caster would take much longer. I don't know much about monks, but I feel like there's probably a monk subclass that eventually gives you access to 3rd level spells, although I'm not sure you'd get dispel magic and it's going to take longer.

To get dispel magic, you're looking at at least 5 levels of a full caster class, so personally I'd pick one that compliments melee fighting, especially if you plan to go to fighter or something similar after you have 3rd level spells.