Well, first off, it's HTR (High Threat Response), not HRT. Small detail, but important.
Think of them as USAF Pararescue (also known as Para-Jumpers, or PJs)... which are the closest thing I can think of in the real world to what a HTR does... and those guys are seriously badass.
To properly simulate a crew of PJs you'll need everyone to be a good medic (DP 8+ before Medkit), as well as have skills such as Diving and Parachuting (which also covers static-line drops from helicopters), and you'll need at least one Rigger to drive and control the support Drones. Other than that... think of an assault team, rather than infiltrators. Their objective is to get in fast, suppress hostiles ling enough to stabilize the target(s) for transport, and GTFO.
Since their positions are "legit" and DocWagon will shield them from repercussions (as long as they don't get "excessive"), that means they don't have to sneak and skulk and beat around the bush. They also don't have to pay for their own ammo. In traditional Shadowrun terms, you're looking very definitely on the Pink Mohawk end of the spectrum, only with flashbangs and gel rounds instead of HE and APDS.
As far as actual starting points and gear, I'd recommend Grand Karmagen (aka 1000-Karma Karmagen), since these guys are going to be by no means "starting out" types, and require them to soft-cap all their physical Attributes. The players should be required to buy their own Cyberware, Foci, and any "personal" gear (private car, off-duty body armor, etc)... but give them an assortment of "standard issue" gear for free, which is only available for use while "on the job".
For the actual load-out, I'd recommend customizing that based on Metatype (a Troll or Ork, obviously, can wear more than a Human), but I'd recommend it look something like this as the basic "human" loadout:
Light Milspec Armor w/ Helmet
-Armor
---Chemical Seal
---Gel Packs
---Nonconductivity (6)
---Responsive Interface Gear
---Shock Frills
---Strength Upgrade 1
-Helmet
---Flare Compensation
---Internal Commlink (6/6/6/6)
-----Suite of Rating 6 utilities + ECCM + Agent/IC for hacking countermeasures)
---Mark 74 Smartlink
---Responsive Interface Gear
---Vision Enhancement (3)
---Vision Magnification
Yamaha Sakura Fubuki - Personal Defense Sidearm
(Stick'n'Shock Ammo)
-Personalized Grip
-Smartgun, External
Ares Alpha - Main Weapon
(Stick'n'Shock Ammo)
(Chemical Round Ammo)
(Flashbang Grenades)
(Gas Grenades - Breathtaker)
-Airburst Link
-Foregrip
-Gas-Vent 3
-Grenade Launcher (Stock)
-Personalized Grip
-Sling
-Smartgun, Internal (Stock)
I admit I may have aimed a little too high-end there, but DocWagon has never seemed to be the kind that skimps, seeing how the DocWagon CRT Helicopter has both an internal turret and two racks for Large aerial support drones.
DocWagon "standard" vehicles are listed in Arsenal (p114-115 & 116) and Unfriendly Skys (p 10 & 11). From what I understand, the Osprey (with some after-market armor and electronics upgrades) or the CRT Helicopter would be what the HTR teams would probably use. I'd recommend a smaller group get the Helicopter, since they'd need the drone support, while a bigger group would use the Osprey.