Melee is mostly bound to weapons and the actual level of your character doesn't matter

Well, if progression is the only thing you care about, spell casters will give you the best experience as a new player because they literally scale as you level up. In fact, the only thing that will give you significant damage boost is going to be the level of your main spell. Difference in damage between a level 20 and 21 spell gem is going to be around ~15% increase. Level 20 vs 24(so a lvl 21 gem with a lvl 4 empower support) would almost double your damage.

Melee is mostly bound to weapons and the actual level of your character doesn't matter. If your weapon is bad, so will your character. There are hundreds of leveling unique weapons and most of them are going to be better than whatever you can get from a spell. Melee doesn't require constant increase in links, either. Just change your crap weapon for a better one and you're set to continue your journey.