Repeating a couple things here as advice for new players:
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You should probably save all the Rare (blue) weapon and armor mods instead of applying them to your gear. You wont have much of your gear for long until later in the game (and the mods are permanent, you can’t remove them or get them back, only replace them), at which point Legendar (purple) mods are the way to go in all but the most specialized of situations. And you can trade three of the same Rare mods for a Legendary version, so Rare mods are mostly going to be more useful as materials for Legendaries later on than as bonuses to your current gear.
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Armor and weapons can be shared between all of your characters. Armor can’t be equipped cross-class, but weapons aren’t class specific. You only need to meet the minimum level requirement for weapons to share across all your characters.
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Items are shared too, so things like faction tokens can be traded in by whatever character you want (useful if you’re trying to complete certain armor sets that only certain vendors can give you, for example all my “Arcology” tokens (the tokens for activities on Io) that I earn with any of my characters get turned in by my Titan since I’m trying to get a specific armor set for him.
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Speaking of sharing your inventory, check out destinyitemmanager.com to juggle inventory between the shared vault and all your characters without actually going to the vault in game. Includes extremely useful filtering options and you can even save load outs for quickly swapping gear.
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Learn the public events! All public events have criteria to turn them into “heroic” public events with greater rewards, and I’m not saying you should go google them all right now, but please make an effort to figure them out if you don’t know how already. Some are pretty easy to work out on your own, and in most events you won’t actively screw something up as long as the other players know what to do. But there’s one specific event I hate hate hate because it’s very easy for well-meaning players to end the event and preclude the heroic version without doing anything obviously wrong.