OK here is my 4 suggestions but first I need to explain some terms
Cover - A barrier that protects against both incoming fire and can provide concealment.
Concealment - Hides the creature but does not protect the creature from incoming fire, like a bush or tall grass. So I would treat D&D 5e half cover and 3/4 cover bonus to AC as types of concealment. So taking these into consideration we can get into your questions
"When you attack a creature from a direction that is not protected by Cover, you gain advantage on those attack rolls. Targets that have concealment still obtain the increase in AC provided by that Concealment"
Example - Bill attacks a Jaffa who is standing in the open without any cover or concealment from a concealed position that provides Bill 3/4 cover. In this instance Bill would have advantage on all his attack rolls made against that Jaffa. If the Jaffa attacks Bill, then the Jaffa would have advantage on his attack rolls but Bills "AC" is 5 points higher due to the concealment he has. If Bills Concealment also provided cover then the Jaffa would not have either advantage or disadvantage but would still need to meet Bills increased AC
The idea is to make player choose their cover wisely and not get caught in the open!
Suppression should be a way to impose disadvantage on your opponents attack rolls or completely remove their ability to return fire. However to effectively suppress a target you need to fire enough rounds down range so it should tied to how many time a creature is shot at during a turn.
A Wisdom save to ignore the suppression could be used as you keep your cool under the hail of fire. Another Idea is that a weapon could have the suppression attack feature which uses an attack action to instantly cause the affected creature to save against being suppressed
My example would be
"When a creature is fired upon (insert balanced number here ed 5) times in a turn or is attacked by a weapon that used the suppression feature that creature needs to check to see if they become suppressed. Make a DC15 Wisdom Save. On success you ignore the suppression as you keep you cool under fire. On a failure you can only make 1 attack at disadvantage on your next turn as you fire blindly in the direction of incoming fire."
Nothing wrong here totally agree.
First thing is what are the damage types available
My thoughts would be (Ball) (Armour Piercing) (Hollow point) (Concussive) (Fire) (cold) (Electrical/lightning) (Acid) and all the other types from 5e.
Next how do those damage types affect a creature. Creatures could have (Immune - attacks do nothing) (Vulnerable - attacks do double) (Resistant - attacks do half) (Not listed - Attacks do normal)
Damage would then be based on ammunition class. Pistol and SMG would be a D4 or D6, Rifle a D8 or D10 A heavy weapon a D12 and explosive could be anything as they are base on how big a bang you want.
You then can make weapons fire a number of times per attack making some weapons better than other however they chew through ammo faster. here is an example of the complete damage model
Bill has a M4 carbine and the M4 has a magazine of AP loaded. The M4 has a damage die of a D8 and is capable of firing up to 3 time per attack with the last two shot at disadvantage. If Bill fired at a Jaffa that was resistant to Ball ammo only, Bill's AP round would inflict normal damage as it was not listed as a resistance or vulnerability. A M4 would use rifle ammo of the 1D8 type.
Bill is able to make two attacks per turn. On his first attack he fires in "burst mode" which fires 3 rounds. 1 normally and the next two at disadvantage. He successfully hits with all 3 rounds and inflicts 3D8 + Dex damage and expend 3 ammo in the process. Bill then uses his second attack action to repeat the process and inflicts only 1 hit of 1D8 + Dex but still expends 3 more ammo in the process.
Does that make sense?