Each Wizard's Arcane Tradition subclass gives them a "Savant" feature:
Beginning when you select this school at 2nd level, the gold and time you must spend to copy a [school] spell into your spellbook is halved.
As well as one or more features that affect or are affected by spells of that school of magic, such as in the School of Conjuration's Benign Transposition:
Starting at 6th level, you can use your action to teleport up to 30 feet to an unoccupied space that you can see. Alternatively, you can choose a space within range that is occupied by a Small or Medium creature. If that creature is willing, you both teleport, swapping places.
Once you use this feature, you can't use it again until you finish a long rest or you cast a conjuration spell of 1st level or higher.
Wizards learn two new spells every time they level up, and they can also copy spells they find into their spellbook (for a cost of gold and time).
My question is: Is it generally more effective (cost/efficiency-wise) for a Wizard to learn spells of their chosen School at level up (to gain access to spells that benefit their subclass features sooner) or to copy them from spell scrolls or other spellbooks later, for a reduced cost?
Best Answer
You're right, there's theoretically a slight disincentive to learn spells from the wizard's own school
You've hit on an interesting conundrum, which is that by making it cheaper to copy spells of a specific school, it's theoretically more cost-efficient to learn spells from schools other than the one you chose for your Arcane Tradition when you level up and then hope that you can learn the spells in your own school by copying them for half price. Essentially, every time you pick a spell in your own school instead of another school, you're shortchanging yourself, because copying that spell would have cost you less than another spell, so getting it for free has less value. If your only goal is to learn every available spell as cheaply as possible, you always want to choose spells from other schools on level-up.
However, this is assuming you can find scrolls or other copies of all the spells you want in order to copy them into your spellbook, which is far from guaranteed. Unless your DM is very generous with giving you scrolls as loot, the only way to guarantee that a spell will be in your spellbook is to pick it on level-up. So in practice, your best move is usually to pick spells based on how useful they will be to you in your adventuring rather than theoretical value. After all, if you cared more about gold than magic, you wouldn't have become a wizard, would you?
Lastly, I'll note that you don't necessarily need a lot of spells from your own school in order to get value from your spell school features. For example, an Abjuration wizard can always activate their Arcane Ward simply by casting Mage Armor at the start of their adventuring day, and doesn't need any other abjuration spells prepared. Obviously they would get slightly more value if they occasionally recharged their shield by casting other abjurations throughout the day, but they will still get value casting only one abjuration per day.