I tend to like the advent carrier and battleship fleet, so my technique is a bit different. I try to guess the enemy's escape route and place my long range ships where they can hit them for as long as possible without eating too much lead, use my light frigates to pound on their flaks to give my bombers clear skies while the flaks pound on their fighters and bombers, then pound their caps with everything I've got. I like to leave my carrier in mid-long range to take advantage of it's abilities and let me swing it in to cover if I need to pull out my battleship. Fill in the gaps on your own if there are any, and realize some bits are rather specialized but some are just good general technique.

Oh, and Arilias, if you don't bring some flaks, you can't muster enough fighters to cover that fleet, so bombers will kill you. painfully.

It's kind of funny, but during four betas I never thought strategy or really used much strategy (econ snowball effect ftw!), but in release I just started using this and it works really well. A TEC carrier will want to stay farther away, it just isn't durable enough, and the vasari carrier wants to get stuck in and use its abilities. Oh, and I use roughly the same fleet as the above, but go for some flaks and one or two of those uber sweet advent shield ships.

Oh, I missed the complete lack of a mass of light frigates in the fleet I referenced. Here's my ideal fleet for the midgame (later ones have more varied caps, tailor them to fit their intended roles and nice synergistic effects).

-1x advent carrier
-1x advent battleship with the ability that makes it a giant firesink
-2x shield restore cruisers (advent only, massive synergy with the battleship)
-a few light carriers or another full carrier, your choice
-gaggles (~40) of light frigates to act as a massive battery of antimatter and provide impressive firepower
-some long range frigates if you want, not really necessary but definitely useful for hurting ships as they retreat
-5-10 flaks, depending on enemy fleet composition because you don't want to waste those massive squads on fighters

use is rather self-explanatory if you're familiar with the ships: just use the battleship as a massive fire sink, use the cruisers to prop it up, and the light frigates to keep both full of antimatter, and use the killing strategies i outlined earlier.

What I am using mid-game is somewhat similar to some others here.

My attack group is usually:

Combat Fleet:
Radiance Battlecruiser x1
Mothership (because it is fairly high level and can colonize after I attack) x1
Destra Crusader x10
Iconus Guardian x5
Defense Vessel x5

Long Range Fleet:
Halycon x1
Illuminator x15
Defense Vessel x5

I have found focus firing on enemy cruisers really destroys their firepower, afterwhich I can focus solely on their capital ships. I've found I can typically take out all the capital ships if I focus fire on them from the start, but I find a lose a lot of my supporting fleet (Ie. cruisers, frigates) which is a pain. For some reason, targetting their cruisers seems to either destroy enough of their firepower to save most of my fleet or refocuses their attacks away from some of my weaker ships. Using this method I can typically take out 1 capital ship (assuming he had 3 or 4). I'm unsure as to which is the reality right now.

What I target first depends on what they have.

If there are significantly more frigates/cruisers than cap ships I will target those first as they die faster and thereby reduce the overall damage output of the enemy fleet faster.

If it is a moderate sized fleet then I will target the cap ships first.

Specifically, if I am using carriers I will target any flak ships to clear the way for the fighters/bombers. I've also taken to killing the LRM or race specific long range ships first in smaller fights, as they usually do more damage than the "workhorse" frigates and die faster.

Essentially, I target whatever I can kill the fastest to reduce the enemy fleets damage output the fastest.

I just started playing yesterday, but I noticed one thing:

I took my very nice fleet and focusfired on one of their three capital ships they had.
As soon as it exploded, the AI re did their threat analysis, noticed the big drop in "oomph" and their chutzpah factor plummeted. They turned around and ran. Ran slow enough, however, that I was able to vaporize another capital ship.

Throughout the game, that was really the tide turn. My fleet then lumbered off from planet to planet, vaporizing them entirely.

You gotta be carefull of the enemy fleet having too much healing capability to take down the caps first.

Its not often, but yesterday there was a fleet with 19 Robot Repair cruisers to go with a Kol and a Dunov along with the usual light frigate swarm. The Kol hops out front as the obvious target, but its just bait. I took out most of the repair cruisers first, then the Dunov with its sheild repair and finaly the Kol.

Of course the repair cruisers are easy to replace, so you have to be sure you can pursue the fleet after wittling them as the main goal is to get at the Caps

It's usually best to target frigates first. Capital ships can escape meaning you suffered casualties for not much achievement. Even if you kill it, frigates are a greater portion of fleet firepower than capitals are - so you will still be taking damage at a high rate.

Focus firing is great, but note that you will lose more damage to mitigation than you might otherwise. Against human players there are specific counter strategies to this as well, like tactical use of Dunovs.

Some splash damage abilities badly punish frigate spam, most notably EMP Charge and Cleansing Brilliance.

Here's a quick list of counters I wrote up.

Fighters are most effective against bombers, long range frigates and siege frigates.

Bombers are most effective against heavy cruisers and planetary defenses.

Light Frigates counter support ships like flak frigates, carrier cruisers, and utility cruisers. They are vulnerable to missile frigates and planetary defenses.

Missile Frigates counter light frigates. They are vulnerable to heavy cruisers and fighters.

Flak Frigates mostly shoot fighters, but are reasonably effective against missile frigates and siege frigates. They are vulnerable to light frigates.

Heavy Cruisers counter long range frigates and light frigates and are excellent general combatants. They are vulnerable to bombers and paralyzer cruisers.