Basic and the 2 Classifications

In Easy Red 2, there is technically no such thing as primary nor secondary weapons. Instead, a soldier will always have 2 equipment slots for their main weapons. These 2 equipment slots can be filled with any 2 weapons. What are considered as main weapons are any guns or weapons (rifles, lmgs, smgs, rocket launchers, etc) that are not grenades.
These 2 equipment slots actually have a label on them, although not really a persistent label. The 2 labels are:
-) "on Right Hand" slot
-) "in Inventory slot"
Below is going to be explanation on how the slots work

Visual Placement on Soldier Model

Any guns currently in "on Right Hand" slot will appear on the soldier's hand (the M1 carbine in the pic). Ready to be used, fired, and reloaded at any time in third person or first person view model.
Any guns currently in "in Inventory" slot will appear on the soldier's back (the BAR in the pic). Ready to be switched into when needed.
You can also check inventory to see what weapons equipped on your character. There will always be at max 2 weapons in your inventory to represent both "on Right Hand" and "in Inventory" slot.
Now while this visual cue works for almost all weapons, pistols follow a bit different rule.
All pistols/handguns don't appear on the soldier when it's in "in Inventory" slot. Keep in mind of this info.

Switching Between the 2 Slots

As mentioned before, these 2 slots are actually not persistently labeled. By pressing the change weapon key (by default 2 key or scroll mouse scroll wheel), your character will switch the weapon in "on Right Hand" slot with the one in "in Inventory" slot. As in the picture above, now the BAR is in the "on Right Hand" slot, while the m1 carbine is now in the "in Inventory" slot.

Picking Up and Equipping

Any weapons picked up into your inventory in Easy Red 2 will always take over the either of the 2 equipment slots. When opening inventory near the gun you want to pick up, clicking on it will show these 2 choices as in the image above, (Take Into Right Hand or Take Into Inventory)

Take Into Right Hand:
Selecting "Take Into Right Hand" will switch out any weapon that the soldier currently has in the "on Right Hand" slot as can be soon on the above picture. The m1917 enfield that was ready to be used is switched with the m1 garand from the floor. Now the m1 garand is the one in "on Right Hand" slot, while the m1917 enfield is on the floor.
Selecting "Take Into Inventory" will switch out any weapon that the soldier currently has in the "in Inventory" slot as can be soon on the above picture. The m1911 that was in the soldier's "in Inventory" slot is switched with the m1917 enfield from the floor. Now the m1917 enfield is the one in "in Inventory" slot, while the m1911 is on the floor.
You can also pick up and equip weapons through quick inventory action, which works the same.