Hello,
Many Members of Hitmans do not know how to correctly purchase Weapons.
Of course you can buy them, at Ammunation, or at the Illegal weapon shops in Chinatown or bayside, but its expensive.
I recommend you to do it this way:
open your Laptop (/portable)
select the menu point Weapon packages ('order')
select a Package you want to buy, and type 'order X', where X is the packages ID.
If can happen that you need to type 'order X' again, because it sometimes bugs.
-> it will tell you that you are done.
Go to the Hitman HQ, where the Armour pickup is placed, and click your Sprint_Key (by default, SPACE, many people use SHIFT though.)
You will the pay the cahs, and get the weapon(s).