Combat skills today are nowhere near as powerful as they were in pre-0.8 because the bonuses are smaller. Also because player cannot be much faster than the enemy to overtake cowardly AI.
Yes, flagship with all personal skills is a bit stronger, but my flagship still struggles to punch above its weight, though not as much as an unskilled ship. However, all that extra combat power does little to fix the greatest obstacle - forcing fights! My combat boosted Paragon or other big ship has trouble against small ships because the AI refuses to engage until it has the numbers to swarm and kill my flagship. (Before 0.8, bonuses were big enough that a battleship could survive, but not today.) Combat skills merely delay the inevitable. If I pilot a smaller ship, the boosts are not enough to let it punch above its weight. I used to solo capitals with a Medusa, and solo cruisers and Onslaught with a Wolf, with pre-0.8 skills. I cannot do that today. Actually, cruisers are still tough opponents for Medusa even with Combat skills. (Also, Medusa has trouble forcing fights against some frigates.)
When trying to solo fleets, the best success I had for that was with a carrier flagship because most fighters are faster than frigates and force fights. To make the idea work, I need max carrier skills from Leadership plus Helmsmanship 3 from Combat so my carrier can run away with zero-flux speed while fighters are "Engaged". (I also have no assault weapons and add Unstable Injector so that my carrier is fast for its class.)
The greatest obstacle to soloing fleets is forcing fights against a cowardly AI that fails to perceive and exploit an overwhelming advantage. You can have all the firepower and defenses you want, but if one side or both plays coward, then the fight may come down to who runs out of peak performance/CR first. Before 0.8, with the combination of Augmented Engines and enemies charging in for the kill, there was usually no trouble forcing fights against the AI, and it was glorious.
All the discussion about flagship affecting battles, player can do that with an unskilled flagship too. Combat skills does not make your flagship significantly better enough to justify the cost of building a Combat specialist.
@ alguLoD: You cannot quadruple your resistance to EMP. Only the Resistant Flux Conduits hullmod offers EMP resistance. Before 0.8, Damage Control reduced EMP damage, and it was great. Probably so much that the benefit was removed in 0.8 so that ships cannot be immune to EMP today. Resistant Flux Conduits is a near-universal top-tier hullmod, nearly up there with ITU and Expanded Deck Crew.
I like to dip into Combat. I get Combat Endurance 1, Evasive Maneuvers 1, and Helmsmanship 3 minimum. Combat Endurance 1 is great when fights are decided on a timer, and they sometimes are given the AI's cowardice. I like to get Damage Control 2 and Defensive Systems 2 too, but lack of skill points make those choices hard - hard enough that I usually do not take them and leave points unspent. If I dip much into Combat, then I cannot afford luxuries like more officers in Leadership, Navigation in Technology, or any of Industry.
Aside, if I know for certain that my flagship of choice is not a carrier, the Gunnery Implants would be a no-brainer for me. However, if my flagship is an unarmed carrier (because they are the best at killing fleets), then all of those juicy weapon bonuses are worthless to me.
Thunders are glass cannons that take too long to regenerate (but they have the best offense for 8 OP). They are most useful for EMP if you do not have Claws to spare. Otherwise, more durable (or cheap) fighters tend to be more useful.
@ TrashMan:
I agree Loadout Design 1 is useless. Loadout Design 2 is useless without Loadout Design 3, due to lack of OP. Once player gets Loadout Design 3, he can often afford super-max vents and Loadout Design 2 becomes useful. However, even if 1 and 2 are useless, 3 is so good that it is almost always worth the cost for everyone. (Without Loadout Design 3, ships tend to have barely enough OP to afford the basics and none of the advanced stuff like Converted Hangar, bombers, and weapons more advanced than Open Market stuff.) It is that good. Only Electric Warfare 1 is a better perk because an automatic -10% to 20% malus to shot range to many late-game fights really hurts, and preventing that is great. (All carrier fleets are not as good as they should be due to AI faults, so having non-carriers to tank for carriers is a good idea.) #3 perk, probably Fleet Logistics 3, is a distant third.
Fuel is a big deal, maybe about as much or more than supplies. For some people, the tandem is too much, especially if they use slow pokes like Prometheus. (I would gladly take the +5 to Sustained Burn, since that is my default mode of travel even for pursuing enemies.) I really, REALLY want Navigation, but because Navigation has no use in a fight (unlike Fleet Logistics), I pass it up because I there are not enough skill points to get everything I want for combat.