Sins version would also help (Vanilla/Entrenchment/Diplo - Trinity is simply all of them in one package, maybe version number). If it's the Diplo Pirates we're talking about, they can be very brutal if they choose the wrong (or right?) upgrades. Entrenchment/Vanilla Pirates can be held off with the right mix of static defenses.

If you need more fleet supply (the initial supply is 100), you need to research more in the Fleet Logistics tab of the Research window. Logistics research doesn't require a particular lab type: it only requires x amount of labs to be present. Be aware that each increase in fleet supply has an accompanying increase in income taxation so as to limit how much upgrading you can do (otherwise your income becomes very small). Initial tax rate is 0%, second is 9%, and so on up to the 8th and final rate, 75%.

I recommend turning pirates off when you're first learning the game.  The game generally plays better without them.  Unlike barbarians in Civilization, pirates will only attack one empire at a time, and for beginner players and lower-difficulty AI (note: hard is considered lower-level) this can usually clinch the game if multiple consecutive raids hit the same victim.  If you ever go for online multiplayer, virtually no one plays with pirates on.

For capital ships, you need both fleet command and capital ship crews, which are a separate research.  This means it's very expensive to amass large fleets of capital ships because of the up-front crew training cost.  Generally speaking 2-4 capital ships is considered the "sweet spot", though in longer games with larger fleets 6 can be pretty common.  The most caps I've ever had simultaneously in a serious match would probably be around 8.

Sticking to one or two planets is suicide.  The benefit from early expansion is absolutely enormous from both a tactical and economic standpoint, and maintaining a large empire is the easiest way to win the game.  One or two in particular is so small that it's questionable whether you could even function effectively.

Expand quickly, and use a mobile fleet for defense.  Avoid spending too much on tech or infrastructure early and stay lean.

Diplomacy Pirates are retarded. The game stops being a game about building a fleet, and starts being a game about building an economy so you can afford to keep bribing pirates.

I am reeeeaally terrible at this game.

I do have the newest version v1.011 (I'm guessing Impulse keeps it up to date automatically).

I've turned the Pirates off, am playing a 1v1 small map (the included one that is randomly generated) as the TEC with a random opponent who I've set at the easiest level with a random personality. It seems whilst I was rapidly expanding, they expanded to three planets, build a massive fleet with a heavily upgraded cap ship, came along and for a while, it seemed my fleet was on par with theirs.

It wasn't...slowly, my fleet started exploding, but not to worry, I had some newly researched missile frigates being build (JAV I think they're called). 8 of the buggers, along with a few Cobalts.

I send them in just after my cap ship explodes, and their remaining rag tag, beat up fleet killed them all as well.

I am terrible at this game.

I think I'm just having balance issues and don't seem to be able to balance my expansion against my research...I don't think I'm doing things quick enough either. Probably a hold over from having plenty of time in games like Civilization, I keep researching/building things then forgetting to research/build something else for a few minutes...this may well be putting me behind.

Love it though, despite being crap.

If you installed via Impulse, you were automatically patched to the most recent version during installation.  If there are patches in the future, you will be alerted via impulse and can patch from there, but it will not automatically patch without your permission.

Eight frigates is not a particularly large fleet.  In fact, that's quite a tiny fleet.  On the random-small map, I'd typically want to have 20-30 of them for my initial push against the enemy.

Sounds like the battle was already a lost cause and you needed to retreat much earlier.  Remember that Sins is a relatively slow-paced game, and that means it will take a while to retreat.  You need to think ahead and start your withdrawal before your capital ship has taken serious damage.

It's very common for people to spend too much on technology.  Unless you're playing on "fastest", you really don't have any business researching anything except unit prototypes and ice/volcanic colonization in the early-game and should be diverting all your cash towards military units and colonization.  Later on tech becomes very important (and on the faster game speeds it can pay off sooner) but early-game on lower game-speeds you need to prioritize military and expansion to the exclusion of everything else.

If you want specific pointers, you can post a replay and I'll critique it for you.

The Vasari Kortul is a suitable battleship, also the Marza and Vulkoras dreadnaught class capital ships are also viable (but only in the hands of master).  Kol, Dunov, Rapture, Revelation, Radiance, and Antorak however are indeed unheard-of as openers among experienced players.

Build some repair platforms.  These will vastly increase the longevity of your ships and in the early-game the presence of a repair platform basically makes capital ships invulnerable; they'll heal faster than they take damage.  You can defeat AI forces that vastly outnumber you with these simple and inexpensive defensive structures, and even after the battle has moved on they make a great place to retreat and recover when injured.

Two repair platforms and a frigate factory built in close proximity is arguably the strongest early-game defense available.  This will keep your defenders alive even when outnumbered, while the frigate factory builds reinforcements to increase your fighting power.  It's relatively inexpensive and extremely difficult to overtake without decisive numbers or staging base nearby.