Melee Champions don't need to change, they simply need more defined itemization.
I think ranged champions are properly defined, and melee should have a slightly hard time getting to them. Below are some unique items that I feel would make Melee champions more viable over all, and give people a more defined build direction that fits fighters better than the current availability.
------Ransom's Mauler: builds from pickaxe, cloth armor, null mantle.
item part costs 875+300+400= 1575/combining cost 725/total cost 2800
40 AD
35 mr
35 armor
passive:Auto Attacks now gain an additional 10-180 bonus magic damage (10(current level)) this effect can not happen more than once every second.
the point of this item is to give tanks and fighters an offensive/defensive weapon that beefs up their auto attacks a little while allowing for their builds to remain tanky. It is also significantly less effective for people who try building aspd because the effect only happens once per second, so they would only trigger it every other (sometimes even every 3rd) AA. Since it is an AA modifier it is also not in danger of abuse through critical strikes.
------Nature's Fortitude: (my take on what FoN should have been)
builds from QSS, chain vest, ruby crystal.
item parts cost 1550+720+475= 2,745, combining cost 555, total cost 3,300
+300 hp
+45 mr
+45 armor
passive: if you receive damage that would drop your hp below 25%, you receive a shield equivalent to (armor+mr)+75 for 4 seconds. This effect can only occur every 90 seconds.
active: removes all debuffs (90 second CD)
this allows resistances to gain a bit more popularity by rewarding having more mr/armor. This item is one that really makes tanks tougher to take down and slow down, but at such a high cost and expensive build path, it won't be fully utilized on anyone who doesn't plan on being a full tank.
------Enraged Flail: (builds from phage and bilgewater cutlass)
2,750 item cost+ 450 = 3,200 total
300 hp
50 AD
15% lifesteal
UNIQUE Passive - Rage: Basic attacks grant 20 Movement Speed for 2 seconds on hit. Kills grant 60 Movement Speed for 2 seconds. Active - Fury's Terror: passive rage is lost for 3 seconds, MS is increased by 50 for 3 seconds, ignores unit collision, and if an enemy champion is within AA range, that enemy champion receives 150 magic damage, and is slowed by 25% for 1 second. (120 second CD)
this allows melee champions who are at risk of being kited to have a small window of opportunity to really close the gap and stick to their targets, while still allowing for counter play through roots, stuns, and even slows. It also allows for some really interesting team fights :) (use active, run in, damage and slow the whole enemy team if they are clustered) it also gives Olaf a new best friend(ult+active synergy), and we all know he needs that.
Honestly any one of these items in any form would make me incredibly happy. I feel like I tweaked them pretty well as far as cost/balance, but I am no professional.I'd love to hear some feedback and concerns, as well as any changes/tweaks that could be made to better these items.