Legion Tactical Support Squads were mobile fire-support units that replaced the utilitarian Bolter of their comrades with more specialised weapons, enabling them to cope with particular battlefield threats or enemies. Operating in close order with the Legion's other troops, the Tactical Support Squad's firepower enabled a battlefield strike force of Space Marines to act with even more versatility and engage a wider range of targets on its own terms.
Nothing more needs to be said about this squad. It acts exactly as its namesake. When utilising this squad; it's role is best suited to accompany the core of your army. This may mean that the squad is equipped with Meltaguns (assuming your army lacks any form of anti-tank); or possibly Volkite Calivers or Rotor Cannons to provide supportive fire etc. Outfit the squad, depending on your army's need.
Usually I'd say take as many marines as you possibly can, but this may actually become too expensive with certain options (like the Plasma Gun and Melta Gun). In these cases, it may be best to take the base 5 and give them a Rhino. Again, take as many marines depending on your needs.
And IMO, luckily this squad cannot be used to fill the compulsory Troops selection slots.
Every model in the squad is initially armed with a Flamer (besides the Sergeant). You might even consider keeping that weapon instead of exchanging it for another Special Weapon.
Rotor Cannon - This is basically akin to a better Heavy Stubber (Salvo 3/4). It's not my first choice due to S3, however the sheer mass of bullets is bound to kill something. Think about it.
Volkite Caliver - This is my first choice of weapons. It has a decent high rate of fire (Heavy 2) and comes with S6. For a supporting fire weapon, this is a very good choice.
Plasma Gun - To me, this is extremely expensive, but really, it's the same cost as any other Plasma Gun, you're just able to take 9 in a full squad.
Meltagun - Same reasoning as the Plasma Gun, very situational and less versatile.
Bolter - Consider it, it's my favourite of the options. Remember you're not replacing anything.
Combi-Weapon - If you like one-shot weapons where if you miss, you don't get another chance, then go for it. Basically, it's one of those "If it's your thing".
Melta Bombs - You can never go wrong with Melta Bombs, take it.
Augury Scanner - This would deter anyone Deep Striking and stop those pesky Infiltrators from infiltrating too close. Situation, but I like it.
Plasma Pistol - Too expensive!!
Power Weapon - Power Sword or Power Maul, your choice. Power Axe would be nice, but I'd rather take the Power Fist.
Power Fist - If you take this, you don't need Melta Bombs. Coupled with Artificer Armour, you can prove to be quite deadly in Challenges.
Single Lightning Claw - I've always believed Lightning Claws should be taken as a Pair or with a Storm Shield perhaps (unless you're in Terminator Armour). So personally, I say no to this option.
Artificer Armour - With the new Challengers, this might actually prove to be a really good choice.
I'd give you a "Suggested Option" however there really is none. It's one of my favourite units in the army due to its versatility. Take whatever options you feel like that suits your army's need.