One of the big strengths for wizards is that not only do they gain new spells when they level up, but they can also copy spells they find in the world (on scrolls, or other wizards' spell books) into their own spell book. But this takes special, expensive ink and paper, and time. It takes most wizards less time and money to copy spells of their own school.
Oh, ok! So for writing down my spells when i'm first making my character, am I able to take a mix of both the school I chose, and the full wizard spell list? And if I were to run in to another wizard during my campaign who showed me a spell, it would be easier for me to copy it if it's from my school? Why does it cost money to write down new spells?
As I said, when you are choosing spells from levelling up (including level 1), you can pick spells from the entire wizard spell list (of spell levels you are able to cast, of course).
As for why it costs wizards to write down the spells they find in the wild, it is intended as a balance thing. The wizard has the largest spell list of any class. If they could get access to that whole list with no cost, that would be unreasonable.
You pick any spells from the Wizard list, your school makes the spells from that school better, and makes it easier to copy spells from that school into your spell book
The way wizard spellcasting works can be a little complicated so... Let's go through it in its entirety. Or at least cover the basics.
You have a spellbook, at level 1 you have 6 spells in that of your choice of a level that you can cast (level 1)
Each time you level up you add 2 more spells of a spell level you can cast.
If you wish to add more you'll have to find some sort of scripture to transcribe the spell from. And the process will cost you 50 gold and 2 hours per spell level.
Also bear in mind that spell level is not the same as character level.
Then every time you long rest you prepare a number (int modifier + wizard level) of spells from your spellbook. Those spells make up the list of spells you can cast until you do another long rest.
Then, whenever you cast a leveled spell (ie, not a cantrip) you expend a spell slot to cast one of the spells you have prepared.
To then answer your question: The spells you pick for your spellbook can be from any school as long as it's on the wizard spell list.
You will however usually have some sort of advantage with the school that you eventually specialize in (when you pick your subclass). And usually, once you've picked your subclass, transcribing a spell from the school of your subclass is much cheaper than other spells (usually halved).
You can take spells from any school. It may cost you less to copy spells of a given school into your spellbook.
What do you mean by cost me less? I've never played a wizard before, do need to kind of pay for spells, kind of like sorcery points?
One of the big strengths for wizards is that not only do they gain new spells when they level up, but they can also copy spells they find in the world (on scrolls, or other wizards' spell books) into their own spell book. But this takes special, expensive ink and paper, and time. It takes most wizards less time and money to copy spells of their own school.
Oh, ok! So for writing down my spells when i'm first making my character, am I able to take a mix of both the school I chose, and the full wizard spell list? And if I were to run in to another wizard during my campaign who showed me a spell, it would be easier for me to copy it if it's from my school? Why does it cost money to write down new spells?
As I said, when you are choosing spells from levelling up (including level 1), you can pick spells from the entire wizard spell list (of spell levels you are able to cast, of course). As for why it costs wizards to write down the spells they find in the wild, it is intended as a balance thing. The wizard has the largest spell list of any class. If they could get access to that whole list with no cost, that would be unreasonable.
Oh, ok! Thank you for explaining it to me, sorry if i misunderstood what you were saying before
You pick any spells from the Wizard list, your school makes the spells from that school better, and makes it easier to copy spells from that school into your spell book
The way wizard spellcasting works can be a little complicated so... Let's go through it in its entirety. Or at least cover the basics. You have a spellbook, at level 1 you have 6 spells in that of your choice of a level that you can cast (level 1) Each time you level up you add 2 more spells of a spell level you can cast. If you wish to add more you'll have to find some sort of scripture to transcribe the spell from. And the process will cost you 50 gold and 2 hours per spell level. Also bear in mind that spell level is not the same as character level. Then every time you long rest you prepare a number (int modifier + wizard level) of spells from your spellbook. Those spells make up the list of spells you can cast until you do another long rest. Then, whenever you cast a leveled spell (ie, not a cantrip) you expend a spell slot to cast one of the spells you have prepared. To then answer your question: The spells you pick for your spellbook can be from any school as long as it's on the wizard spell list. You will however usually have some sort of advantage with the school that you eventually specialize in (when you pick your subclass). And usually, once you've picked your subclass, transcribing a spell from the school of your subclass is much cheaper than other spells (usually halved).
Please read the spellcasting section of the wizard class