Spell you should show your player:
Catapult - use acid, alchemist fire, or even just oil (followed by the player's preferred fire spells) to kick an extra bit of damage on a 1st level spell.
Cause Fear - I know it's concentration, but giving a creature with multi-attack disadvantage is huge for your allies.
Grease - requires some work, but in a narrow passage, it can keep enemies from closing, or allowing your front line to pound on prone opponents. Everyone needs ranged attacks though, because smart enemies will simply withdraw behind it.
Levitate - concentration, but this can also be a great offensive spell against an enemy lacking ranged attacks. You put them up about 60 ft until the end of combat, then either pelt them with ranged attacks until they surrender/die, or let them drop from 60 ft for 6d6 damage, then have your melee buddies pound as a reaction on the now prone enemy.
Web - concentration, but useful for holding some enemies out of the combat, then he can fireball them afterwards, dealing extra damage
Counterspell - no wizard should forsake this. While it's not an action, it will suck away those fireball slots
Hypnotic Pattern - you'll kick yourself for doing this, because this is probably the most amazing control spell in the game.
Melf Minute Meteors - your player might really enjoy it, as it can potentially deal more damage than fireball. It'll also allow him to use his bonus action.
Slow - probably a better choice for you as the DM than Hypnotic Pattern, but does the same type of control (just not as bad)
Banishment - not only great for getting rid of pesky outsiders, but taking a target out for the entire combat, then pounding on them when you bring them back is pretty awesome.
Evards Black Tentacles - basically Web with damage
Polymorph - offensive or defensive, this spell is amazing. Make an ally into a killing machine or make a powerful enemy into a shark while on land to take it out while dealing with the rest.
Wall of Fire - the most evil use of this spell (which you're player will love) is using the 10 ft radius Ring configuration on a paralyzed/restrained target(s), with the damage pointed inward. Even when not using it this way, it still works into his theme.
Animate Objects - a bandoleer of daggers becomes a quezenart that shreds one monster at a time.
I always liked burning hands and thunderwave. They are close range and get multiple bad guys. Most wizards do not like to be that close, but they come in handy.
Burning Hands may be good, but I detest Thunderwave. I refer to it as "ringing the dinnerbell"