Characters on Terraria have no leveling system.
If you call leveling getting higher hp I would recommend you grabbing Heart crystals which are found in the underground zones this will increase your health +20 at a time until you reach 400 max hp.
For Higher Mana you should collect fallen stars these can be combined to make Mana crystals which increase your Mana by +20 at a time. You can have upto 200 Mana at a time.
For armor you either craft it from Ores or find it from bosses. Eater of worlds will drop atleast 1 piece of armor at a time.
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Copper Armor - Weakest - 160 copper ore
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Iron Armor - 225 iron ore
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Silver Armor - 300 silver ore
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Gold Armor - 360 gold ore
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Meteorite Armor - 540 Meteors - Regenerates mana - Set bonus - Space gun: No mana required
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Necro Armor - 90 bones (from dungeon) and 135 cobwebs (underground) - Set bonus: Increase overall speed by 20%
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Shadowscale Armor - 440 Demonite ore (from bosses and from terrain) and 56 Shadowscales (From Eater of worlds) - Set bonus - Increase melee speed by 15%
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Jungle Armor - Silver armor set, 90 jungle roses, 12 stingers, 4 vines, 8 amethyst, 8 topaz, 6 rubies, 6 diamonds, 10 sapphires and emeralds - Hard to collect as its in the jungle and the average damage from monsters is 20-50 - Slow mana regeneration - Set bonus - 25% reduced mana usage
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Molten Armor - Gold Armor set, 105 Hellstone Bars - Strongest armor - Set Bonus - 15% extra melee damage.
For weapons just search chests for them and if they are materials you can upgrade them. Place them in the Guides crafting section and then it will tell you the materials required to make them.
Hope that helps
-Inferndragon