So, for fun, I made a build based on how I would do this concept ... no melee, but other than that its a burnout mage.
Backstory is the same as the OP's - worked for a corps (Ares), had x happen (shadowrunners, accident, whatever). He lost an arm, and his eyes/ears. Getting them replaced cost him his essence, and his life savings. Ares didn't pay for it (of course) and had an over abundance of meat muscle so let him go. Now he needs to shadowrun to pay the bills.
Overall he's actually pretty solid, at least in combat. Very good dicepools in automatics and heavy weaponry, he can bring the hurt in a firefight. He brings some utility to the team with his spellcasting as well - 12 dice for health spells isn't shabby. He's decently sneaky and perceptive, but not much of a talker (stereotypical street sam).
He's defensive enough to also last a bit. He could use some more armor, but thats not too hard to acquire down the road. He's spent 2.3 essence, so he's got .7 more he can spend before he takes another hit to his magic. He could raise up his basic skills, but thats not a bit karma investment. I sort of like him.

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Priority:
A - Attributes
B - Nuyen
C - Magic (Mystic Adept)
D - Skills
E - Metatype (Human)
Attributes (could flip reaction and strength)
Body - 5
Agility - 8 (6 base + 2 from bioware)
Reaction - 4
Strength - 5
Willpower - 5
Logic - 1
Intuition - 5
Charisma - 1
Edge - 3
Essence - 3
Magic - 2 (bought with Karma)
Derived Values:
Mental Limit - 4
Physical Limit - 7
Social Limit - 4 (+2 more from armor?)
Condition Boxes: Physical - 11
Condition Boxes: Stun - 11
Condition Boxes: Overflow - 5
Armor - 16
Positive Qualities
Mentor Spirit - Bear
Agile Defender (probably not necessary)
Restricted Gear (Cyber Grenade Launcher)
Negative Qualities (need 25 points, can play around with this)
Unusual Hair
Corp Limited Sin (Ares)
Combat Junkie
Skills:
Automatics - 6 (SMG Specialization) (+1 from reflex recorder) - Dice Pool: 15 (17)
Heavy Weapons - 6 (Grenade Launchers) - Dice Pool: 14 (16)
Spellcasting - 6 (Health Specialization) (Health Mentor Spirit) - Dice Pool: 8 (12)
Perception - 1 (+3 for audio/visual from cyber) - Dice Pool: 6 (9)
Sneaking - 2 <-- bought with karma --> - Dice Pool: 10
Etiquette - 1 <-- bought with karma --> - Dice Pool: 2
Knowledge Skills:
English - N
Magic Theory (Academic) - 3
Ares Security (Corp) - 4
Japanese (Language) - 2
Combat Trids (Interest) - 3
Tradition: Egyptian (because why not!

But really, any INT+Will tradition works)
Spells:
Increase Reflexes
Increase X (agility, strength, whatever)
Heal
Levitate
Some Combat Spell (whatever you want, really - this is just for fun)
PowerPoints:
Combat Sense (II) - costs 1 point
Karma Breakdown:
32 karma remaining after qualities
15 Karma = Magic 2
5 Karma = 1 PowerPoint
6 Karma = Sneaking 2
2 Karma = Etiquette 1
2 Karma = Sustaining Focus I
2 Karma = Sustaining Focus 1
0 Karma remaining
Contacts:
Ares Headhunter - 2 connection, 1 loyalty
Gear:
Fake SIN (IV)
Fake License (IV) - Firearms
Fake License (IV) - Magic
Low Lifestyle (1 month)
Certified Credstick (Silver)
Datajack
CyberEyes (III)
Image Link, Camera, Smartlink, Thermographic Vision, Low-Light Vision, Vision Magnification, Vision Enhancement (III)
CyberEars (II)
Sound Link, Damper, Spatial Recognizer, Select Sound Filter (II), Audio Enhancement (III)
Full Obvious Cyberarm (L)
Base Agility 6, Base Strength 6
Cyber Grenade Launcher, 10 grenades of varying type
Muscle Toner (II)
Reflex Recorder (Automatics)
Sustaining Focus (Health) (I)
Sustaining Focus (Health) (I)
Reagent - 100x Dram
Suzuki Mirage
Meta Link - burner commlink
Transys Avalon w/Sim Module
AR Gloves
Berwick Suit
Argentum Coat
Forearm Guards
Ares Sigma Six - SMG from Gun Heaven 3
Ammo x100
Ares Alpha - Assault Rifle
Ammo x100
Grenades x10
Ares Crusader II - Machine Pistol
Ammo x100
Medkit (Rating IV)
~5000 nuyen left to play with