Alright, here's a very quick build without all of the more personal choices made (like contacts, knowledge skills, and a few qualities).

Done with Sum to 10: EAEBB
Without taking into account money or nuyen you earned, since this build doesn't need to be that exact. It's a "mundane" augmented vampire. Chummer seems to think the Vampire initiative bonus stacks with Wired Reflexes. I don't think it's supposed to, but that's up to your GM. This guy has skills to get into a good position for an ambush, and will basically never go down in combat. His 24 armor means basically all damage is Stun, so whatever bits get through won't kill him. Pain Editor stops him from falling unconscious; when your Stun track is full, it goes to Physical at a 2-1 ratio (so, it takes 2 Stun to do 1 Physical box) and you don't accrue wound penalties. Meaning, basically you have really high damage mitigation and can take three times the damage a normal person can before going down, and the damage you take never slows you.
This build isn't as deadly with their fists as the adept, but is still a threat, enough to feel like they aren't helpless without a gun by any means. With the smartgun, they have 16 dice for firing in Semi-Automatic mode, so they're a good shot. This is mostly just the skeleton of a build, but it should give you an idea of how you could do it.
== Personal Data ==
Name: Unnamed Character Alias:
Human
Movement: 18/30 (2m/hit)
Swim: 12 (1m/hit)
Composure: 6
Street Cred: 0 Judge Intentions: 10
Notoriety: 1 Lift/Carry: 11 (90 kg/60 kg)
Public Awareness: 0 Memory: 6
Karma: 0 Nuyen: 10,684¥
Age: Skin:
Eyes: Hair:
Primary Arm: Right
== Priorities ==
Metatype: E,0
Attributes: A,4
Special: E,0
Skills: B,3
Resources: B,3
== Attributes ==
BOD: 5 CHA: 3
AGI: 6 INT: 5 (7)
REA: 3 (5) LOG: 3
STR: 4 (6) WIL: 3
EDG: 3
== Derived Attributes
Essence: 0.09 Initiative: 12 +4d6
Physical Damage Track: 11 Rigger Initiative: 12 +4d6
Stun Damage Track: 10Astral Initiative:
Physical: 8 Matrix AR: 12 +4d6
Mental: 6 Matrix Cold: 12 +3d6
Social: 4 Matrix Hot: 12 +4d6
Mortimer of London: Argentum Coat: +1, Must be visible
Securetech PPP: Arms Kit: -1, Must be visible
Securetech PPP: Legs Kit: -1, Must be visible
Astral: 6
== Active Skills ==
Con (Fast Talk) Base: 3 + Karma: 0 = 3 Pool: 6 (
Etiquette Base: 3 + Karma: 0 = 3 Pool: 6
Gymnastics Base: 2 + Karma: 0 = 2 Pool: 8
Navigation Base: 3 + Karma: 0 = 3 Pool: 10
Palming Base: 6 + Karma: 0 = 6 Pool: 12
Perception Base: 4 + Karma: 0 = 4 Pool: 11
Pistols (Semi-Automatics) Base: 6 + Karma: 0 = 6 Pool: 12 (14)
Running Base: 2 + Karma: 0 = 2 Pool: 8
Sneaking Base: 6 + Karma: 0 = 6 Pool: 12
Survival Base: 3 + Karma: 0 = 3 Pool: 6
Swimming Base: 2 + Karma: 0 = 2 Pool: 8
Tracking Base: 3 + Karma: 0 = 3 Pool: 10
Unarmed Combat Base: 6 + Karma: 0 = 6 Pool: 12
== Knowledge Skills ==
== Qualities ==
Biocompatability (Cyberware)
Dependent (Nuisance)
Family Curse
Infected: Vampire (Human) (INT)
Restricted Gear
Uneducated
Vendetta
== Critter Powers ==
Allergy (Wood, Severe)
Allergy (Sunlight, Severe)
Dietary Requirement (Metahuman Blood)
Dual Natured
Essence Drain
Essence Loss
Immunity (Age)
Immunity (Toxins)
Induced Dormancy (Lack of Air (Essence) Minutes)
Infection
== Cyberware/Bioware ==
Bone Lacing (Aluminum)
Datajack
Internal Router
OrthoskinRating 4
Pain Editor
Smartlink
Wired ReflexesRating 2
== Armor ==
Helmet +2
Mortimer of London: Argentum Coat 14/+4
+ Concealability
+ Custom Fit (Stack)
+ Gel Packs
Securetech PPP: Arms Kit +1
Securetech PPP: Legs Kit +1
== Weapons ==
Infected Bite
Pool: 12 Accuracy: 8 DV: 7P AP: -1 RC: 3
Savalette Guardian
+ Smartgun System, Internal
Pool: 12 (14)Accuracy: 7 DV: 8P AP: -1 RC: 4
Unarmed Attack
Pool: 12 Accuracy: 8 DV: 8P AP: - RC: 3
== Commlink ==
Hermes Ikon (ATT: 0, SLZ: 0, DP: 5, FWL: 5)
+ Commlink Functionality [Camera, Micro 1, Chip Player, Credstick Reader, Earbuds 3, GPS Guidance System, Micro Trid-Projector, Music Player, RFID Tag Scanner, Shock- and Water-Resistant Case, Touchscreen Display]
== Gear: Equipped ==
Ammo: APDS (Heavy Pistols) ×48
Ammo: Gel Rounds (Heavy Pistols) ×36
Fake SIN Rating 4
Spare Clip (Savalette Guardian) ×6