When beginning a new co-op or team-based game like The Division, I typically dive right into medic, mostly because healing others is both a good way to get people to like me and a good way to hide the fact that I'm not great at shooting. Reviving fallen friends (or strangers) doesn't require a medic: any player can pick up a fallen agent and get them back on their feet. But there are some great abilities that make reviving other players quicker, easier, and more effective for all you aspiring medics out there. Here are the best abilities to aim for.
First Aid with the Booster Shot mod
This lets you heal a player or players by launching what is essentially a health bomb at them, which restores health to anyone standing inside a small radius. From my experience, it's good to let a player know it's coming. (James, a very active and nimble player, often proved an elusive target for my electronic healing hugs.) The Booster Shot mod, meanwhile, also grants the players you heal an increase in the damage they deal, allowing them to quickly drop whoever is trying to drop them.
Support Station with the Life Support mod
This works a bit like First Aid, but instead of firing a projectile you can place the station at your feet or fling it to a particular spot. While it's active, it creates a small radius that continually heals both you and any player within range, which is great if you're going to be hunkered behind a particular piece of cover for a bit.
There's a mod called Ammo Cache that turns the station into an ammo dispensary as well as a healing zone, but quite honestly there are so many ammo crates in the game, especially at the location of boss fights, it doesn't feel completely necessary. Instead, go with the Life Support mod, which can revive any fallen friends who crawl into its radius, extremely useful if several members of your team get trounced at the same time and you can't risk running out of cover to save them.
Signature Skill: Recovery Link
Once you've got First Aid and Support Station, I'd recommend knocking out medical side-missions as fast as you can. Stockpile your Medical Wing Points until you've earned 1,000 of them so you can unlock the Disaster Aid section of your base. This will grant you the powerful Recovery Link Signature Skill, which essentially turns you into a mobile hospital. Upon activation, it creates a large radius around you which heals both yourself and any player in range. It also revives downed agents and can "overheal" your teammates. The cooldown period is extremely long so this is to be used only in grave emergencies.
There are a number to choose from, but here are the four most effective ones for the medic. Combat Medic, which means when you use a health kit on yourself, any friends standing nearby also get healed. Pharmacy, which reduces incoming damage by 50% for 10 seconds for both you and the player you're reviving, which means there's less of a chance you'll both be immediately downed again. Triage, which reduces the duration of skills cooldowns by 15% when you heal a friend. Finally, Critical Save will increase your own damage resistance by nearly half for 10 seconds, useful for when you have to run out of cover to bring a pal back to life.
Key Stat: Electronics
I'd really like to recommend you focus on Stamina, since medics need to be as durable as possible, but focusing on electronics will give your various healing gadgets better properties: increased range, faster heals, and so on. Look for gear, or craft gear, with good electronics attributes: it'll help you save more lives.