For a hand crossbow "gunslinger" Variant Human Battlemaster Fighter:
STR 14
DEX 17+1
CON 15+1
INT 10
WIS 16
CHA 12
Take Perception as your Human bonus skill. Take Athletics and Acrobatics as your Fighter skills. Pick up Stealth and another skill of your choice from a Background. Take Archery as your Fighting Style.
I'd go Crossbow Master at Level 1, granting you two attacks from the start, and allowing you to attack with your Hand Crossbows at close range if needed. Then Sharpshooter at Level 4, extending the useful range of your Hand Crossbow to a respectable 120 feet. With a DEX of 18 from the start, you can afford to wait until Level 6 to bump DEX to 20.
Wear Light Armor, carry several Hand Crossbows, and have a Rapier for backup.
You'd be an effective short to medium ranged attacker, with your bonus attack helping to make up for your lower damage compared to a Longbow. (2 attacks from Level 1-4, 3 attacks from 5-10, and 4 attacks from 11+.) You'd also be an effective party Scout.
I'd consider dipping Ranger for 2-3 levels to get an extra skill, the Defense fighting style for +1 AC, Hunter's Mark for +1d6 to each of your attacks, and Darkvision plus some ambush bonuses from Gloomstalker if you go 3 levels. Or alternately, you might consider dipping Rogue for 1 level to get an extra skill, some Sneak Attack damage, and Expertise in Stealth and Perception.