This is a quick list of what battlepack you get at what level.

Level 3, 5, 7, 12, 14, 16 & 18

Bronze Battlepack (3 random items)

Level 22, 24, 26, 28, 32, 34, 36 & 38

Silver Battlepack (4 random items)

Level 10, 20, 30, 40, 42, 44, 46, 48, 50 (and every level beyond)

Gold Battlepack (5 random items)

The Bronze, Silver and Gold Battlepacks can contain the following:

Random attachment for any weapon (unlocked and not)
Random paints (for weapons/vehicles)
Random camos (for soldiers)
"Exclusive" weapons (like knives)
Experience boosts (25%, 50%, 100% and 200%)
Dogtags
Avatars/portraits (pointless really)
Emblems

r/battlefield_4/comments/1q8lfy/battlepacks_levels_and_you/?sort=confidence