Any items you get can be used between all your characters. Keep anything that is A or S rank for sure. You will learn as you play, what items are useable for your class and for classes you aren't going to play, do not pay to identify them. Later on you can start tossing common items away as you will have a lot of S rank gear. Starting up I kept everything C and better. Once I started playing online I only keep A rank or better, and again only if my characters could use it.
As you play you will be able to buy bags which let you have multiole sets of equipment. You can have up to 9 bags which you can set various potions, weapons, and gear into. Once you start doing infernal difficulty and maybe even on hard, you can set your bags for each dungeon. When you start doing chain runs (doing multiple dungeon paths without returning to town) you will need more bags because you are not going to be able to repair your gear. Before you start the dungeon, each player is ablr to select what item bag they will use for that dungeon.As a bonus you can add gear that gives damage and defensive bonuses depending on the dungeon. So one bag can be good against dragons and you use it when you fight the red dragon, and one might be strong vs undead which helps when you fight the reaper. With my elf I have 9 bags with two weapons per bag. One weapon is general purpose and I switch to the other for bosses.
It seems like a lot to grasp but basically keep any weapons and gear for your class that is better than what you have until you start buying bags. Then keep stuff to fill your bags and as you do more chain runs (best done online) you will get enough decent equipment to fill an entire bag with S and A rank items. This happens because the score and money multiplier goes up each time you continue your adventure and do not return to town. A good group can chain until they max the multiplier and continue this for 10+ runs and really rake in the money and gear. I think my max was 3 hours non stop and we ended up with over 100,00,000 gold since we S ranked each dungeon path multiple times.
This is an example of what your character should look like when you progress enough. This is my Elf with 9 full bags.