The first thing you'll have to unlock is the Luger. To do this you must get 10 kills with the Push Daggers melee weapon, and once you've completed this you have to claim the rewards in the Side Jobs section on Crime.Net.

Once you have unlocked the Luger, you need to unlock the MP40. This is achieved by getting 50 kills with the Luger. Once you have done this you need to claim the rewards from the Side Jobs tab on Crime.Net.

Now you must purchase the MP40 and kill 100 enemies with it to complete your journey. After you claim it from the Side Jobs tab of course. Congratulations! You now have access to purchasing the M1 Garand. You can find it in the Assault Rifles tab.

Well, my recommendation would be getting the Surefire skill to base, giving your Galant 15 extra rounds in the magazine! (The cops fear the power of the 23-Round M1 Garand.)
Another thing you can do with your Garand is you can complete the "The Control's Hundred Tab" Side Job, which can be completed by killing 200 enemies with your Galant.