My input is more of what I see with a wizard, and in turn have made my wizard (a sylph as well).
There is an old old guide to playing a wizard and I think it is still relevant, if you want me to link it to you then I can. Right now I'm going to summarize what I have gleaned from it.
As a wizard, you can really focus on several different roles.
1. The blaster - this is an evocation specialist who essentially just sits back and nukes.
2. The controller - here, instead of just blasting with your spells, you are controlling the battle field.
I like the 2nd option. Here you are using things like obscuring mist, gust of wind - things along that lines to control where the enemy is at and how they can react. The other vital part of this is the summon monster spell line.
As a sylph you will notice that one of your racial abilities is Air affinity
Air Affinity: Sylph sorcerers with the elemental (air) bloodline treat their Charisma score as 2 points higher for all sorcerer spells and class abilities. Sylph spellcasters with the Air domain use their domain powers and spells at +1 caster level.
While not a requirement, this almost leads you to the air elemental school as well as the proclivity to summon creatures with the air subtype.
I find the air elemental school to be cool. The only down side is that earth is the prohibited school. The biggest hit is the loss of Acid Splash which is a nice 0 level damage spell.
https://www.d20pfsrd.com/classes/core-c ... hools/air/
One of the best perks is fly at will at 10th level. The spells are also a nice mix of control with a few blasting spells
-Gust of wind will help control airborne creatures as well as ranged - archers and such
-Wind wall will help keep enemies separated until the need to bring them into the fray.
-Lighting bolt, shocking grasp, and chain lightening are your blasting spells
-And it has the summon monster line.
All of these at a Caster Level at +1 which means your summons last an additional round, your damage is as if you were 1 level higher, the duration is longer so on and so forth.
Now I've hinted a lot at summoning monsters. As a wizard (or a cleric for that matter) I tend to focus on this. Consider the Damage over time or something else to do than just cast spells. And a lot of the monsters give you additional things to do during your round. Oh, and it is not hindered by Spell Resistance
So, I usually build summoners and the sylph actually turns into a fairly good one.
So, to start off you may look at the following build.
Feat - Scribe Scroll - Bill may not let you take this one - since we said no crafting - so instead Spell Focus (conjuration) - it's a feat tax, but allows you to take
Feat - Augment Summoning - Now your summoned creatures are at +2 Str +2 Con and are a bit more viable.
1st Spells -
Mage Armor - I noticed you had leather armor on your wizard - this will give you a 10% base spell failure - meaning each time you cast a spell you may lose it. Mage Armor fixes this for the wizard.
Magic Missile - a great go to spell that always hits - not affected by air affinity - but still nice to have
Obscuring Mist - I know people give flack for this one, but it's a great early control spell. As a Sylph you can see in the obscuring mist, and careful placement will let you divide a group of monsters and you will still know where they are.
Shocking Grasp - Touch spell - but one that you can increase the CL of.
Take note - I don't want to tell you how or what to play - but I have had a lot of fun with this build. It kept me doing more stuff in a round than just casting or shooting my crossbow.
Oh and I had to laugh that as a Chaotic Neutral character you took the god of Law as your deity