When you get your weapons to level 5 and 10, you can buy a new weapon at the appropriate shop. When you get your weapons to level 15 and 20, you will automatically receive a quest to get a more powerful weapon. As for getting new weapons in general, you unlock them as your notoriety increases. You get the dagger unlock quest at level 10, grenade unlock quest at level 20, and staff unlock quest at level 30. Also, you won't be able to train in the warehouse... only killing enemies will work.
