GreenTengu
Adventurer
I am really surprised at the really bad job people do at figuring this stuff out.
Okay, first-- for a Wizard? Strength is absolutely worthless. You couldn't wear armor or use a shield if you wanted to! As long as you can carry your gear, you are fine with a 8 Strength and it will never come into play against you.
Also, I believe you do need 1 hand free to cast any spell with anything but verbal components.
This is two strikes telling you NOT to use a 2-handed sword. The few extra points you might squeeze out of a two-handed weapon's base damage die just simply is not worth it.
What you DO need as a Wizard is good Dexterity. You need the initiative, you need the extra points of AC, and you need a good Dexterity save which you are likely going to be making a couple times a session. Stealth and Sleight of Hand (to pull out those magical components without drawing attention) are pretty indispensable to any wizard since if you can avoid being targeted for damage at any time, it saves you precious HPs.
So since, if you have any idea what you are doing, you are already going to be loading up your Dexterity attribute anyway-- then any martial weapon you get should be one that uses that attribute rather than require you to raise an attribute you otherwise would not.
So the first martial weapon you should always choose is the Rapier. Same damage as Longsword, but to-hit and damage are based on Dexterity. It leaves your hand free for casting without having to sheath or drop it.
The second weapon you should choose can either be
1) A long bow-- deals a bit more damage, but it is heavy and two-handed so if you want to switch between shooting and casting, you have a problem.
2) A hand crossbow - far more ideal for switching between casting and shooting, but it is a loaded weapon which means you have to use your bonus action to reload it. Though I don't believe as a Wizard you will lose out on anything there.
Now-- as for school, even though Volo's guide pushes Evocation, that is the absolutely worst choice. Since some part of your character's "points" for a lack of a better term have been used to invest in martial weapons, the last thing you want is for your magic school to effectively give you a better direct damage option than relying on them at all times. But, you have the advantage that you are going to be dealing more damage than any other wizard with your basic weapons-- even better off than the lauded High Elf or Mountain Dwarf.
Since your biggest drawback is that you don't really have a lot of hit points, even with a Constitution boost, Abjuration as others have said is the best option as its basic ability effectively grants you additional hit points. By having focused on Dexterity as I listed above, you are also going to have the higher AC and the Dex save to keep those extra hit points for longer.
But, really, Divination, Necromancy, Illusion and Enchantment are also very strong contenders, you just have to be a bit more creative about how you go about using your abilities than straight-up getting bonus hit points.
Regardless, your top 3 attributes are Dexterity, Intelligence and Constitution (and whether Dex or Int is your #1 is up to you) and the other three can pretty much be ignored. I think I would recommend Wisdom being your next if one is going to be higher than the others and you should put absolutely no investment in Strength as it will almost never come up during the course of the game. Not unless you are going to be required to swim or climb. Even then, if you choose to make Athletics one of your skill choices, you are covered.
Okay, first-- for a Wizard? Strength is absolutely worthless. You couldn't wear armor or use a shield if you wanted to! As long as you can carry your gear, you are fine with a 8 Strength and it will never come into play against you.
Also, I believe you do need 1 hand free to cast any spell with anything but verbal components.
This is two strikes telling you NOT to use a 2-handed sword. The few extra points you might squeeze out of a two-handed weapon's base damage die just simply is not worth it.
What you DO need as a Wizard is good Dexterity. You need the initiative, you need the extra points of AC, and you need a good Dexterity save which you are likely going to be making a couple times a session. Stealth and Sleight of Hand (to pull out those magical components without drawing attention) are pretty indispensable to any wizard since if you can avoid being targeted for damage at any time, it saves you precious HPs.
So since, if you have any idea what you are doing, you are already going to be loading up your Dexterity attribute anyway-- then any martial weapon you get should be one that uses that attribute rather than require you to raise an attribute you otherwise would not.
So the first martial weapon you should always choose is the Rapier. Same damage as Longsword, but to-hit and damage are based on Dexterity. It leaves your hand free for casting without having to sheath or drop it.
The second weapon you should choose can either be
1) A long bow-- deals a bit more damage, but it is heavy and two-handed so if you want to switch between shooting and casting, you have a problem.
2) A hand crossbow - far more ideal for switching between casting and shooting, but it is a loaded weapon which means you have to use your bonus action to reload it. Though I don't believe as a Wizard you will lose out on anything there.
Now-- as for school, even though Volo's guide pushes Evocation, that is the absolutely worst choice. Since some part of your character's "points" for a lack of a better term have been used to invest in martial weapons, the last thing you want is for your magic school to effectively give you a better direct damage option than relying on them at all times. But, you have the advantage that you are going to be dealing more damage than any other wizard with your basic weapons-- even better off than the lauded High Elf or Mountain Dwarf.
Since your biggest drawback is that you don't really have a lot of hit points, even with a Constitution boost, Abjuration as others have said is the best option as its basic ability effectively grants you additional hit points. By having focused on Dexterity as I listed above, you are also going to have the higher AC and the Dex save to keep those extra hit points for longer.
But, really, Divination, Necromancy, Illusion and Enchantment are also very strong contenders, you just have to be a bit more creative about how you go about using your abilities than straight-up getting bonus hit points.
Regardless, your top 3 attributes are Dexterity, Intelligence and Constitution (and whether Dex or Int is your #1 is up to you) and the other three can pretty much be ignored. I think I would recommend Wisdom being your next if one is going to be higher than the others and you should put absolutely no investment in Strength as it will almost never come up during the course of the game. Not unless you are going to be required to swim or climb. Even then, if you choose to make Athletics one of your skill choices, you are covered.