I think that every race should have different kind of weapons and armor so not everyon has full platemail, a lion or knight shield and a firesword. Heres some of my ideas:
Humans: Mainly swords, and maybe some axes. Moderate leather/metal armors
Elves: Bows, and Elvin blades (that are one sided blade swords like samurai swords). Many cloth items, like cloaks that make it hard to 'see' them, so you dont hit them as often.
Dwarfs: Mainly axes, clubs perhaps. Mostly metal, and some leather armor.
Orc: Mostly axes and clubs, and some swords. Mostly metal, and some leather armor.
Lizardmen: Perhaps claws to put on their hands? Some sort of hard skin because lizards dont wear armor, or clothes.
Halflings: Probably daggers. Mostly cloth items like clothes.
Just because they are different items, doesnt mean they should be better than eachother. But if they were, it would give people more reason to choose each race, like if one race was faster, one was stronger, one had better armor, ect. Well those are my ideas so far.