My game would be a hybrid FP/TPS, but with heavy emphasis on customization; think Battlefield mixed with Blacklight. Note that this post is really long.
Pre-emptive tl;dr: Read it if you're interested.
The viewpoint could be switched between first-person and third-person, with not much difference between the two other than the actual view.
A lot of different settings would be tunable; though you do have the standard difficulty levels with preset settings, there would also be a "Custom" level which allows you to review the various elements of gameplay and tweak or switch them off, then figures out how difficult the game will be based on that.
There is a very, very heavy element of customization for both the player and the firearms he wields; I think of it as sort of like Gunsmith from Ghost Recon: Future Soldier, only with a heavier emphasis on customization for the firearms, where you snap attachments like supressors, scopes, and extended magazines onto the gun to provide various bonuses or different playstyles. Customization means you could pick the specific type of grip or red dot sight you think looks coolest. You could also change the weapon's base stats by switching out different barrels or stocks, and then you can personalize the firearm by painting it; this can be as simple as putting CADPAT forest camo onto it, to as advanced as putting line art or using a free-brush.
The people are also very, very customizable, with varying armor and underclothes selectable, all of which can have their paintjobs selected from preset or custom-made. Nothing is stopping you from running into battle in a stripperiffic outfit; that being said, wearing skimpy clothes means that you don't have armor and that translates to being cut down very, very quickly, which means wearing armor makes it easier on you. Armor works simply; heavier armor absorbs more damage but reduces your mobility.
Same goes for vehicles; what you are driving/flying can have different paintjobs or weapons. For example, the weapon on top of a tank could be an automatic grenade launcher (high damage, but slow fire rate), a minigun (doesn't do much damage but tears environment up with high rate of fire), or a Browning machine-gun (a go-between). You can also customize armor, which has varying effects; higher armor makes you slower, but more resilient to dying.
The actual gameplay is rather simple for an FPS. Iron sights are a requirement to use, but enforced in a different way; weapons are near-perfectly accurate, with no spread as in Call of Duty; however, the closest you get to a hipfire crosshair is a stream of light going from the barrel that marks where the bullet hits, movement makes the gun sway, which makes the stream and thus the impact point sway, and that means it's often better to use the iron sights for more precision targeting (not to mention that beyond the Easy default setting you don't even get that). Of course, crosshairs and leaf sights are available for weapons that can't sight in otherwise. There is bullet drop and Battlefield-style supression, and health… well, the exact level and how fast or if it regenerates is one of the things that can be specified.
Team-mates are also present, and actually intelligent; in addition, they have different commands depending on what you equip them with (i.e. people with machine guns can be ordered to supress, people with grenade launchers or mortars can be ordered to shell an area). Of course, teamies can also be replaced with friends in co-op.
The preset difficulties have different styles of play and are geared towards different people;
Training – Sort of a Call of Duty experience. You have a lot of health (average 5.56 assault rifle kills in 20 hits), which regenerates six seconds after being successfully hit by enemies. Hipfire bullet-line is present, and enemies are rather simplistic in AI. If you go down, you can pull out a sidearm and shoot back at enemies with the ability to shoot yourself back up.
Posting – A Battlefield-esque experience. You have the health of a multiplayer CoD player (5.56 AR kills in 6 hits), which only begins regenerating after fifteen seconds of not being hit or supressed. Your precious bullet-line goes bye-bye and enemies get a fair bit smarter. You are unable to shoot yourself back up when you're down, but you can still be healed by allies or get up if you aren't hit for about 30 seconds. Enemies are also a fair bit more intelligent, able to act smartly on their own.
Battle – A challenging, more realistic experience. You now have the health of a multiplayer Battlefield 3 player (5.56 AR kills in 3 hits), and health has limited and very slow regeneration; you can only regenerate 25 HP sections of your health bar, and you have to use healing items scattered about to heal yourself for the most part. You cannot get back up after going down and must be healed by an ally. Enemies can now act smart both alone and in groups.
Special Operation – For the sadomasochists who play ArmA. You can die in one or two hits from any firearm, and health doesn't regenerate; big enough impacts can drain health over time unless healing items are used. If you go down, you are unable to shoot back and must wait for an ally to revive you, and if they don't do so fast, you die.
Multiplayer plays mostly like Battle, only with Posting's health regen rules and Spec Op's rules for going down, though you can tweak settings as they go. The modes center around Deathmatch (get x number of kills as a team or alone), Conquest (think along the lines of Battlefield), and Objective (which involves getting item A, which can be anything from a bomb to a VIP, to area B, which could be a pick-up point or a reactor). Killstreaks would work on a time-unlock system and would be requested instead of immediately deployed; players who have massively fallen behind have a near-100% chance of getting something called in, whereas someone leading the pack would have trouble getting anything beyond a UAV equipped with radar called in due to their excellent performance. In addition, there would be less killstreaks due to the fact air vehicles are pilotable.
Finally, there is a class system, but it's more loose than anything else; Pointmen have no equipment but move faster and are intended to run distractions; Medics carry gear to heal and revive team-mates, and get innate health regeneration, Supports carry more ammo than base, can restore ammo, and are intended to keep enemies down under constant barrages of gunfire; and Pilots are intended to drive vehicles, and can regenerate vehicle armor as well as move faster and get more armor (though Pilots can still shoot people and the other classes can still drive). There are no weapon restrictions; besides gear, any type of gun can be carried by any class.
Alternatively, if that was too much for you; Star Wars: Battlefront III, because who doesn't want that?