It can be hard when you’re starting from scratch. You’ll have to use what you can find in the level to finish the first few missions. Try to take your time and always check your surroundings to avoid getting caught. When you get caught, try to analyze how it happened and how to avoid it next time.
You can collect guards’ weapons and some other items lying around in the levels to bring back to the safehouse and future missions for free (check the Freeloader thread for a full list). Most of those weapons will not be silenced but better than nothing. Go to Dubai early to pick up a silenced, concealable SMG, which should help a lot. Sgail can give you a silenced pistol.
With time, your collection will grow so that you always have something available even after a campaign failure. You will also unlock new areas of the safehouse that have items or allow you to craft them that you can bring along as well.