We've already taken a look at the things that the Wizard class automatically grants you, so let's dive into the features that allow you to make a choice and see how you can benefit from them.
This is the name given to the Wizard's subclasses – each of them will be fully explored in its own guide. You gain your Arcane Tradition at level 2.
How you tailor the list of spells you know depends very much on your choice of Arcane Tradition, and so this will be covered in more detail in each of those subclass articles. However, you have some choices to make immediately at level 1, so there are some guidelines that you can follow when making those choices.
First up are your cantrips. Make sure you choose at least one cantrip that can deal damage at range as this will be your go-to for attacking enemies, particularly at early levels. Firebolt is the most powerful, clocking in at 1d10 damage, but it's also worth considering Ray of Frost, which slows an enemy down and can make it harder for them to get close to you. After that, you're free to build your toolkit however you'd like. Shocking Grasp gets a special shout out, due to its ability to help you escape from melee situations you didn't want to be in.
Unless you chose a Gnome, Vedalken or Mark of Making Human and scored an 18 at some stage when rolling for your stats, it's very likely that you won't be able to prepare all 6 spells that you're allowed to have in your spellbook at level 1. If you bear this in mind when picking your spells, you can actually turn this to your advantage, though. How, I hear you ask? Wizards are clever fellows who are able to cast spells with the Ritual tag if they are in their spellbook, even if they're not prepared. Such spells are utility spells rather than combat nuke spells, and you should mostly only need to cast them when you have time to cast a ritual spell (10 minutes).
Examples of basic ritual spells at level 1 include Alarm, Comprehend Languages and Detect Magic. Arguably even more useful are Identify and Find Familiar, although it's worth noting that both of these spells will require you to actually buy components to be able to cast them, due to the rule that where a spell component has a cost in Gold Pieces, you can't substitute in an arcane focus or component pouch. (Also, the components for those spells cost up to 50GP! Ouch!)
For the slots that you can prepare, there are a number of spells that will be useful in general. Mage Armour and Shield are both protective spells that will boost your AC (Mage Armour will do it on a more permanent basis than Shield, so if you have limited slots it may be worth going with that one!) Magic Missile is a spell that's been the Wizard's bread and butter since the early days of D&D, giving you a damaging spell that automatically hits.
You have options to control the battlefield too. Sleep is a clutch pick at early levels – it has the power to send large numbers of low level monsters for a nappy nap, right in the middle of a pitched battle. Depending on your party, you can then either tiptoe around them to escape, or brutally murder them while they're prone and snoring. Tasha's Hideous Laughter is a good way to control a larger single target, reducing it to fits of hysterics while, again, the party makes with the stabbing. Cause Fear is a great spell to protect yourself with too if you've somehow angered the DM or their minions have decided they like the taste of spellcaster flesh. Thunderwave is a spell that you'd hope not to be using often, but if you do find yourself surrounded, you can blow your way clear with a lot of noise and general spectacle.
A quick mention for Chromatic Orb here – this is one of those spells that you'll be hard pressed to cast in your first game session because it requires a costly accessory for you to be able to fire it off, but this spell has one of the most impressive damage quotients for a single target without saving throws coming into the equation. On top of that, you get to choose the damage type, so very few creatures will be able to resist it every time it's fired. Its damage at level 1 isn't bad, but if you're crazy enough to chuck at level 9 slot at it, it could open a few eyes pretty wide if you can roll well.
At 18th level, you can choose one 1st level spell and one 2nd level spell from your spellbook to be able to cast at their lowest casting level at will without expending a spell slot. Anything that adds to the number of times you can cast spells is great, being as that is what a Wizard should always want to do. When it comes to choosing the spells, remember that you're not able to upcast the spells you picked with this feature unless you spend a spell slot as you would for a normal cast, so choosing something that does not benefit from being cast at a higher level is going to be your best bet.
For your first level spell slot, if you're of a defensive persuasion, you can pick Shield – from this point forward, if you are hit by an attack you can grab yourself +5 to your AC for free. For your level 2 slot, something like Misty Step or Mirror Image would be ideal for some free mobility or increased defences.
And because you liked Spell Mastery, you get more of the same as your capstone Wizard ability at level 20. You can now choose not one, but two 3rd level spells from your spellbook that you can cast once each for free. They recharge after a short or long rest. (Sorry, no infinite free uses for this one!) Just as with Spell Mastery, you can't upcast these spells, so bear in mind that if you pick something like Fireball, you will always be rolling basic damage. There are lots of cool choices here in various categories – the same logic about choosing things that don't scale holds reasonably well here too, and also bear in mind the fact that you can cast ritual spells without having them prepared. Your best bet for making a choice, being as this hits you at 20th level when you will have been playing for a considerable amount of time, is to ask yourself which 3rd level spells you use most of all. Slow is a great example of a non-scaling spell that can help you a great deal in combat, as is Blink, which can also add even more to your Wizard's survivability.
...and of course Fireball is also level 3 and you don't always need to upcast that to get ridiculous amounts of damage out of it, so you could, yanno, just go for that...