Level reward card is what you can obtain by leveling up characters, including gems, cards, skills, extra deck slots. Which cards and skills you acquire is different according to which character you get to level up.
Level reward details
A table below describes what sorts of reward and how many of each you can get by leveling up a character to 30 (current max level).
Extra deck slot
Level reward tier list
Basically a tier list below shows cards and skills that do a fairly good job regardless of a theme of your deck. That means useful level rewards for you will differ from the list if you have a specific theme on your deck. For example, Mai Valentine should be the first to farm for you to build a Wind deck, since you can get Harpie monsters and supports by leveling up her.
You should level up characters in this tier to 20-25 regardless of a theme of a deck you use.
Card/Skill you should get
[Skill] Switcheroo Shuffle 1 card from your hand to the Deck, then draw a card. The skill can only be used twice per Duel.
[Skill] Life Cost 0 You can use the skill when your Life Points are 1000 or less. You do not have to spend Life Points to activate a card until your opponent's next turn ends. You can only use the skill once per Duel.