Ready and rolled up for adventure, you are ready to enter the Dungeons & Dragons game with your new wizard.
What are a few starting game challenges for a wizard class?
Hit points, spell management, and damage output.
Hit points are the starting point for all wizards, arcane casters, and magic users in the game. At the mid to higher levels you get access to spells and abilities like mirror image, blur, stoneskin, etc. but at the early levels one hit can literally kill you.
As a mage you need to pay attention to positioning in combat. While the fighters and brawlers in the party will be engaging most encounters head on, and you will (should) be in the back of the party stack, wizards are vulnerable to missile weapons.
Stay aware of what looks safe, and what really is safe.
Spell management is next.
Lower lever spells and less of them at the lower levels.
If possible avoid direct damage dealing spells.
Area effect or control spells are more potent and have the ability to tactically effect more in the game during an encounter.
Hitting one orc with a single magic missile.
Charming that orc with charm person.
Sleeping a few orcs with a sleep spell.
Early one, damage spells that you do take can be augmented by throwing daggers and slings since you should be in the back or the party.
As you get some coin, purchasing some low level wands of magic missile, rays of frost, etc. will help expand your damage.
And finally, something to boost extra spell slots like a pearl of power.