Some rough notes…
HEROIC MODERN CHARACTERS
Starting character stats (realistic): 14, 13, 12, 11, 9, 7
Starting character stats (heroic): 16, 15, 14, 13, 11, 9
* +2 proficiency bonus
* Choose any four from among skills or other proficiencies (tools, vehicles).
* Choose one skill, tool or vehicle proficiency to gain Expertise (double proficiency bonus to +4). Weapon proficiencies may not take this benefit.
The Tough Hero
* 1d10 Hit Dice
* Proficiency on Strength and Constitution saving throws.
* Once between short rests, regain 1d10+1 hit points as an action.
The Cunning Hero
* 1d8 Hit Dice
* Proficiency on Dexterity and Intelligence saving throws.
* Pick two additional skills (six total).
* Pick one additional proficiency (skill, tool or vehicle) to gain the Expertise bonus.
SPECIAL COMBAT ABILITIES
Defensive Intuition: Add +1 to your Armor Class.
Martial Arts: Use Dexterity instead of Strength for unarmed attacks, which cause 1d4 + Strength or Dexterity modifier damage. Also, when making an unarmed strike with the Attack action, as a bonus action make another unarmed strike.
Sneak Attack: Once per turn, you can deal an extra damage to one creature hit with an attack if you have advantage on the attack roll. The attack must use a finesse or a ranged weapon. You don’t need advantage on the attack roll if another enemy of the target is within 5 feet of it, that enemy isn’t incapacitated, and you don’t have disadvantage on the attack roll.
Superior Shot: Gain +2 bonus on attack rolls with ranged weapons.
Superior Strike: When making melee attack with two-handed weapon, reroll damage results of 1 or 2 once and take the second result.
Superior Leadership: As a bonus action, give one creature within 60 feet a d6 that can be added to one of its own ability check, attack roll, or saving throw if used within 10 minutes. The creature can wait until after it rolls the d20 before deciding to use the die, but must decide before the DM says whether the roll succeeds or fails. A creature can have only one Superior Leadership die at a time.
Swift Speed: Increase base movement rate to 35 feet.
CHANGES TO SKILLS
Intelligence (Arcana) also includes the occult, secret societies, conspiracy theory and possible knowledge about extraterrestrial aliens.
Intelligence (Nature) changes to Intelligence (Natural Sciences) which includes both life and physical sciences – biology, chemistry, physics, geology, astronomy and so forth.
Intelligence (Religion) changes to Intelligence (Social Sciences) which includes religion plus psychology, anthropology, economics, politcs and so forth.
Wisdom (Medicine) also includes pharmacology and some overlap with natural life sciences – various types of biology, biochemistry, genetics and so forth.
CHANGES TO OTHER PROFIENCIES
In most modern societies, all characters gain proficiency in Vehicles (Automobiles) to drive cars, trucks and similar vehicles. Tractor-trailer rigs, motorcycles, race cars and other such vehicles may be included automatically or added with downtime learning, with the DM’s permission.
Other options to learn should include Vehicles (Powered Watercraft) for boats, ships and submarines; Vehicles (Aircraft) for fixed-wing planes, jets and helicopters; Vehicles (Spacecraft) for rockets and ground-to-space shuttlecraft.
Characters with law enforcement, military or hunting backgrounds can select Weapon Proficiency (Firearms) to use the modern guns described on DMG p. 267-268, but this proficiency does not extend to Futuristic items.
To use explosives, a character must learn the Tools (Explosives) proficiency.
While any character may use commercial computers, the Tools (Computers) proficiency should include hardware to build and modify digital equipment as well as software skills to write and change programs, hack into secure data networks and crack digital encryption.
CHANGES TO HEALING
Use the “Slow Natural Healing” and “Gritty Realism” rules on DMG p. 267:
SLOW NATURAL HEALING: Characters don’t regain hit points at the end of a long rest. Instead, a character can spend Hit Dice to heal at the end of a long rest, just as with a short rest.
GRITTY REALMISM: This variant uses a short rest of 8 hours and a long rest of 7 days. This puts the brakes on the campaign, requiring the players to carefully judge the benefits and drawbacks of combat. Characters can’t afford to engage in too many battles in a row, and all adventuring requires careful planning.