If someone rushes you, he's vulnerable somewhere.  You always need to have some fleet from the opening bell, unless you are shielded by allies from all comers.  If he's got HCs, you've had time to get enough bombers to counter them.  (hangars, carriers, SBs)  If illums, use fighters (and you should still have had enough time to amass some.)  But  But you should also have a few cruisers (even just a dozen or so cobalts) to send in behind the rush and do some damage.  Taking out his constructors is always nice.  If someone rushes you, you've got to make him feel the pain.

I they're rushing with HCs and LRFs, you'll need a more balanced defense, but again, if he's got HCs, you've had time to research that.  As a matter of fact, does it make sense to talk about a heavy-cruiser "rush?"

First and foremost, you absolutely must scout.  Know what your opponent is doing so you can be ready to counter it.  Rushing with destras is a very risky strategy that involves building five military labs early on.  This takes up a huge amount of logistics space and resources, and leaves your opponent very vulnerable to a fast rush.  Spotting it before it happens is important so you can either prepare with the right units, or attack it before it happens.

Now, as for unit types.  Assailants, LRM's, and Illuminators are all "long range frigate" class units.  This means they are great against your basic light frigates.  They are weak to fighters (from carriers) and heavy cruisers.  Destras, Kodiaks, and Marauders are all called "heavy cruisers".  They're virtually imprevious to all types of attacks with one exception: bombers (also from carriers).  Some units, such as the hoshiko with demo-bots, have special abilities that are great at disabling big expensive units like heavy cruisers.

If you can't get a significant amount of strike craft, the only way to defeat these units with by attrician.  The hoshiko is your best unit, and with demo-bots (and enough anti-matter upgrades) that will even put an end to the threat of heavy cruisers.  However, you will have trouble beating heavy cruisers without bombers.

One of the biggest mistakes people make in this game is trying to be an economist too early.  Most of the economic upgrades simply aren't worth the cost of the civic labs until later in the game.  In fact, you're almost always better off putting your time and energy into colonization.  Someone who colonizes extra planets rather than building trade ports will actually earn more money. 

It's possible to HC rush, but typically yes, if you see HC's chances are this isn't a rush but something later in the game.

If you're playing as TEC, get armor upgrades. TEC are masters of close-in ship-to-ship fighting. If its early, put in a Kol, lots of LRMFs and Cobalts. if they have carriers, cut back on your cobalts and build gardas. If they have heavy cruisers, you should to. Build them. Kodiak squadrons are more effective then the other HC squadrons.