The game is quite ambiguous about who are the good guys.  The story we're presented is told by a TEC soldier, so it inherently puts them in a good light, but when you look at how the factions behalve I tend to think they're all on the same moral level.  They go around forcibly subjugating every neutral planet, and indiscriminately kill civilians with orbital bombardment.  It's not called Sins of a Solar Empire for nothing, you know.

Safe bet.

Here's my advice: expansion comes first.  You need to set out to claim your empire early, with a special focus on economically and strategically important planets.  If you see a choke point, you need to go for it. 

Early game the best way to build an economy is to acquire planets.  The best way to protect those planets is with a fleet.  Use repair bays to bolster your defenses and keep your fleet in fighting shape.  Avoid expensive economic infrastructure until you can really afford it.  By the time you're pursuing higher end units, such as carriers and heavies, your expansion should already be largely complete.

As for units, there's one you're missing out on:  the Hoshiko!  It's the #1 reason to play TEC; basically a mobile repair bay.  Arguably the best unit in the game.  Use long range frigates (Javelis LRM for TEC) as your damage and back them up with other unit types, and you're good to go.

Now for capital ships, the Kol (the battleship you're using) is a decent choice in 1.00, but as of the most recent version it's probably one of the weakest in the game.  The problem is that virtually every other capital ship has been buffed significantly, but the Kol has barely been touched at all.  As a result it's migrated from being slightly above average to being one of the worst capital ships in the game, simply because everything else got better.  The Sova, Akkan, and Marza are the staples of the TEC faction currently.

• LF = light frigate (Cobalt and equivalents)
• LRF = long range frigate (Javelis and equivalents)
• SF = siege frigate (Krosov and equivalents)
• HC = heavy cruiser (Kodiak and equivalents)
• SC = strike craft (fighters and bombers)
• Egg = Jerrasul Evacuator (deadly Vasari capital ship)
• Nanos = nano disassemblers (ability of the Egg that makes it so deadly)
• TK = telekinetic push (deadly ability of the Advent Halcyon capital ship)
• GW = gravity well
• neutrals = neutral extractors found in uncolonizable gravity wells
• pocket = a player who begins with allies protecting both his flanks (ie, free to pursue early economy)
• suicide = a player who begins in a 2v1 situation.  With entrenchment, not so much suicide as besieged.
• SB = starbase (used as both a noun - a starbase - and a verb - to starbase)
• PUG = pick up game (method for choosing teams.  Very common online)

If you're playing as TEC, you need to lean on the Hoshiko.  It's your only saving grace against the Advent.  If it goes late game, you need high level capital ships and abilities.  The TEC fleet is largely helpless against a fully mature Advent fleet and will depend on having the right special abilities available.  Unfortunately, TEC lacks a counter to the repulse ability, and so their fleet (I mean this literally) gets tossed around like rag dolls in late game battles.

As Vasari, your trouble against Advent will be early game.  Vasari lack a solid counter to long range frigates, and Advent has the strongest long range frigate.  If you can make it past this stage of the game, Vasari can seriously challenge a fully mature Advent in a straight fight.  Subverters, phase stabilizers, and phase missiles (the holy grail of fighting Advent) will give you the edge to match the sheer power an Advent player will bring to bear.

The best thing you can do against an Advent is to shut down their capital ships.  Their frigates are really strong (particularly the illuminator), but its the support abilities of their capital ships that really set them apart.  If you can force their capital ships to withdraw, or better yet destroy one, your chances of winning a battle skyrocket. 

This is very true; the AI plays Advent horribly, and if anything it's at its worst when using this faction.  I was describing how to play against a human Advent player, who will be maximizing the faction's synergies.  Totally different scenarios.

Finest Hour and Flux Field are also awesome abilities, but they don't hold up to missile barrage (heh, I forgot, MB = missile barrage is another acronym) and armistice.  Yes, I should have clarified that I was speaking about those two abilities in particular.

Yes, I'll add a few more abilities to the acronym list...

FF=Flux Field (reduces AM cost)

FH=Finest Hour (makes the Kol immortal)

CB=Cleansing Brilliance (Advent ability that deals tremendous damage to one target)

SR=Shield Restore (Advent ability that keeps their fleets alive.  It can be found on their colonizer, the Progenitor.)

D_P=Deploy ____ Platforms.  Could be missile, could be siege.  Just insert the correct letter.

PM=Phase Missiles.  Though this is not an ability, but rather a weapon type, these weapons are special in that they have a chance (dependent on research level) to bypass shields and mitigation, thus vastly decreasing the value of shields and is a monstrous help to killing the Advent since they can buff both Shield Mitigation and have massive shield defenses anyways..  Without that, they are quickly killed by the Vasari.

SM=Shield Mitigation.  Perhaps the trickiest subject in the game to understand.  Basically, as you take more damage, this number goes up.  As this percentage goes up, it reduces the incoming damage by that amount.  So 30% SM yields a 30% reduction in damage.  Generally goes up to around 60-70% depending on the ship/race you are talking about...  SM still applies even after the shields have been defeated however.  For this reason, it is generally quite hard to kill an Orkulus Starbase's (or Orky as most will call it)  First, you have SM.  Then you have armor (which is a 5% redux in hull damage per point).  Then you have the ability that it can use called Frontal Deflector Shield which neutralizes 75% of oncoming damage.  The result is that hull damage on the Orky is far less than what you actually deal to it.  If I remember right, I think its around 4%...

This is pretty much my take on it as well.  If anything peryhaps the Advent are the good guys since they're merely seeking justice.  However they're also seeking revenge and religious conquest, so are they really the good guys?  I like Darvin's take on it--they're all pretty much morally equivalent.

The militia are the good guys Joe.  They only defend their own grav well, and they only bomb planets to destroy new and vulnerable alien colonies.  Thats engagement rules, ethics in combat.  I'm afraid if you want to join the elite warlords club then you'll have to abandon such niceties.  You might feel uneasy about it for a while, you get medals and shiny boots though. 

What I recommend is to play some multiplayer 1v1 before trying the team games- Storm Front is a good 1v1 set map.  Once you can put up a strong performance 1v1 you'll be ready for larger games.