At BS13, this is an excellent platform for heavy weapons. To get most of the mileage out of them, run a fireteam (core or Haris) in Corregidor There is a whole slew of weapon options that can all find a use in an offensive fireteam.
The heavy rocket launcher: The only weapon with a positive range modifier outside of 24" in the team. In the active turn at B3 (in a link team) this is an effective weapon with a blast template, that can be used to exploit your opponents' deployment mistakes. The main downside here is the heavy SWC tax (2). When your opponent gets up close, blast away with the assault pistol
The spitfire: Works great in the active turn when the team makes it up the field.
Combi + Light flamethrower: the profile most seen on the wildcat (basic, Lt, N2, . It is excellent at providing your opponent with poor choices.
Boarding shotgun, stun grenades: A fantastic profile if you make it across the board.
The assault hacker: The assault hacker is an excellent assault hacker, he's affordable, has high BTS and decent WIP (13). The only downside is his movement, which can be compensated by using deployable repeaters and/or remotes /morans with repeaters.
ARM 2: average for medium infantry
BTS 6: excellent especially against weapons targeting BTS
V: Courage, allows you to automatically pass the guts check.
Heavy Rocket Launcher: a weapon with a template and the potential to cause multiple wounds, can get B2 with the link bonus
Light flamethrower is excellent at protecting your flanks from AD troops
D-charges: Most profiles come with D-charges, which make accomplishing the sabotage classified objective feasible, especially as most wildcat fireteams do best when they run up the table
Their use in hunting party: Running a core team is an excellent choice in this mission, the whole team gets adhesive launchers, an engineer can be used to un-glue some of your other specialists
Against a TAG: use the assault hacker to immobilize the tag and then run your entire link team in close combat and CC with D-charges.
The main downside of the wildcats is their slow movement speed and lack of long range weaponry. In narrow approaches, this may mean that the controlling player may need to switch link team leader several times to get the right piece in play, leading to a loss of efficiency. This team is very good at shooting, so forcing it to dodge is preferable. Perimeter weapons and mines slow them down more. For direct engagement use flamethrowers or chain rifles to catch multiple profiles in the blast template. As they carry their own flamethrowers, preferably use a cheap warband.
When players run the wildcats, they will often run a Lt profile (the cheapest 0 SWC lieutenant). If the opportunity presents itself (as they move up the board new attack vectors should open up), take it out, it's kind of fragile.
The Lieutenant profile is a cheap 0 SWC profile that works well in Corregidor. In Vanilla it generally gets overlooked in favor of an interventor. It can be run without a fireteam as well, it is an obvious Lt choice. Running a single combi+LFT profile is a good decoy profile for a Lt, especially against shasvasti or haqq.
A defensive haris fireteam can be composed of: Haris + Lt + Heavy rocket launcher. The rocket launcher is there to provide AROs, the Lt hides and the haris profile watches the flanks.
An offensive haris should have a spitfire, specialist and the fireteam haris option.
A full 5 man can be composed of any of the profiles, but I would include at least one heavy weapon (HRL or spitfire), one specialist ( type depends on the rest of your list). Using the Lt in the team is tempting as it avoids having to invest in another Lt profile with potential SWC cost. It forces you to be even more careful when maneuvering.
If the team is meant to be run as an offensive fireteam, they should be deployed in such a way that allows them to approach the midfield without taking too many long range ARO's. Do not allow your spitfire to be outranged in the reactive turn. The only truly scary aro piece that can be left out for long range AROs is the heavy rocket launcher. Use the profiles with shotgun and flamethrowers to watch corners.
A defensive fireteam (typically haris) uses the HRL to watch a firelane, in cover. When including the Lt in this, hide him as best as you can. The haris profile can be used to watch a corner.
Active Turn Role
Try to move and shoot with them as a move-move order has some significantly reduced efficiency. If you're running a mobile team with specialists, grab the objectives and lock down the midfield.
The HRL is the best ARO piece in the team: B2 in a link, the blast template ignoring the cover ARM mod, potentially inflicting mulitple wounds, catching multiple enemy models (especially against link teams)
The boarding shotgun, combi+LFT are great for watching corners and your backfield.
The spitfire is difficult to use as an ARO piece, it's hard deploying him where he'll always benefit from good range modifiers. His role is attacking.
Use the assault hacker in ZOC or through repeaters to stop or slow down the advance of enemy tags, remotes, HI or hackers.