Upgrade and equip one weapon in each of these slots to the top level for that slot, usually 4:
1 Pistol (upgrade this first for explosive ammo, much fun)
4 Explosive (eg annihilator)
5 Special (Level 4 sniper costs $200k before discount..)
6 Melee (baseball bat, level 2)
7 Thrown (any of the 4 grenades, but upgrading flash bangs is best as it gets you the Fart In A Jar weapon needed for the Stay Classy achievement)
Tips: make sure you own the gun store you buy the upgrades in for a discount. If you wait until you complete deckers.die mission you'll get another 25% discount. Money can easily be earned early on by going to the airport, stealing a helicopter from the pads opposite the gang activity and then repeatedly flying the barnstormer at the North end of the runway for $5,108.