Honestly it seems like you have choosen probably the hardest combination of era and faction in the mod to begin your playthrough. New Republic can be very difficult in era 1 for new players exactly for the reasons you have listed.

So generally I would recommend starting in later eras before you get more experience.

What difficulty are you playing on and have you enabled "cruel ai"? As far as I know the "cruel ai" modifier provides the ai with an income boost, which usually allows them to build up fleets faster than you.

I have played the NR on earlier versions (2.3.3 I think, currently I am playing as the Grater Maldrood) on the biggest GC starting in era 1 (though I did not enable "cruel ai" at the beginning). I am not claiming to be an expert, but here is some advice.

My advice would be to always play aggressively in the beginning of your campaign. I usually build one boarding shuttle immediately on Mon Calamari and if possible a second one as soon as possible. Due to the discount provided by Mon Mothma Mon Calamari should be your main production site for ships at the beginning (In general you should try to use discounts as much as possible, since they can save you a lot of credits).

Then gather all your ships you have around Mon Calamari and move south. Try to board as much capital ships as possible during your early battles (even dreadnoughts are better than nothing). Your goal should be to rush the Eriadu Authority and secure the southern part of the galaxy as quickly as possible.
Use your fleet over Endor to attacke the Eriadu Authority from the left. Destroy any undefended shipyards you can find (though I tried to not destroy capital ships with this fleet becaus I wanted to capture as many as possible). Use Bothan spies, if you are uncertain whether to attack.

There are a couple of planets suited to build up an early economy like Nal Hutta and Bespin (I usually build mines on planets that have a hight basis income, though I don't know whether it acutally scales). Trade stations are rather inexpensive in my opinion.

The other pockets of planets that you have like Hast, etc. should just try to hold out as long as possible and deal as much damage as possible to anyone trying to conquer it.

Many of your planets will be unprotected during the early stages but that is nearly inevitable in any campaign. Fortifying alle your planets is too expensive. It is easier to reconquer lost planets. I even lost my capital in one game and still won later on.

As far as units go, Quaser carriers are rather useful. Y-Wings are excellent bombers to deal with enemy capital ships. Usually, the NR fields the best fighters an bombers. I think MC80 Home One ships are too expensive and cost too much population to be build. Rather build a few MC80 or MC80b.

Generally agree with Aushilfsgott, except for boarding crafts: too expensive for early creditless stage in my opinion. I did pretty well without them in 2.3.3 version on captain difficulty.

From the beginning I'd recommend taking every planet in Kessel-Nal Hutta-Ylesia for some income - your initial forces on Mon Calamari and Hast are more than enougth to do that.

Don't bother building anything like barracks and factories on rear planets, you won't need tons of ground forces if the ground assaults are played carefully (i.e. reveal with heavy tracker and bomb 'em to the mud). Concentrate on already developed worlds (Chardaan, Sullust, if you can keep them). Nal Hutta has lots of building slots and can become an excellent training ground.

Don't bother to make stationary defences unless you have a decent fleet protecting the border planet (ground ion cannon might be only excpetion). I usually queue MC80b, Home One type and MC80 on Mon Calamari and keep such production order till the Era 3.

AI starts to act on week 4 or 5, so prepare to blitzkrieg Eriadu Authority by that time. Secure the space above their planets and put a non-stealth disposable unit (I prefer infantry) there to prevent the AI from building a space station. Once you hunt down every hero (be wary of Delvardus with his Praetor-class, he is a tanky one), the EA won't be a threat. And with their planets becoming yours the hard stage of New Republic playthrough is over.

Here's a tip about protecting borders: do not keep a defence fleet on the border planet itself! Have it orbiting the nearst system instead (Mon Calamari for Hast, Honoughr for Kessel, Bespin for Endor). The AI sees there's no defence and sends an ordinary battlegroup instead of some faction's entire armada of any flying junk it could spare. So as you get a signal "enemy fleet approaching", just move the fleet to the postion with sinister laughter: "It's a trap!" :D

Use CC-7710 in your defence to utterly decimate the invading fleet. Besides, those corvettes are pretty cheap capacity and costwise, unlike Interdictors. A mere presence of gravity well will prevent the AI from retreating.

And some other stuff:
Firmus Nantz has enougth starting forces from his chunk of NR territory to defend Endor from Empire of the Hand (using the border protecting tip listed above). Sometimes if gets tedious, though.
Sell barracks on Mon Calamari and build Mon Calamari shipyards as ground structure. Now you can remove Mon Mothma somewhere else and build MC's with 30% discount instead of Mothma's 25%.
Don't dump all your fleet on the enemy during an attack, use the vanguard slot (that square in the top left corner of the fleet window). I usually place CC-7710 or some corvette there to reveal the battlefield and use the ability to hyperspace my fleet to gain positional advantage. Hyperspacing to the rear of a SSD is the most efficient and the only safe way to destroy it.
Don't defend Contruum and Generis, it's pointless. Sell all the ships orbiting the planets along with ground forces and structures, except for Senator's office. Sell it when an enemy fleet is approaching the planet. WARNING: if you sell the office in the beginning of ground invasion inself, you will automaticlly lose the next battle you're going to participate in. Some sort of a bug.

Hey Everyone

Thanks a bunch for the useful tips.
Some of them I figured out on my own. Some I will implement.

I'm still not 100% happy with the behavior of the A.I.
The big Stacks still are "unbeatable" for a long portion of the play through but the A.I. will leave most of their planets undefended.
So once you are able to beat those Stacks, you basically can steamroll your opponents.
So it's either f*ck*ng hard or way too easy.

In my play through, only the Pentastar Alignment invested in defense platforms or a more varied mix of big capital ships and smaller support ships and as such was the only faction with interesting tactics to beat.
So the game play is still not really satisfying.

Another thing that bothers me (this is a common problem with all mods I've played) is that on land battles, the A.I. reacts so fast, that making a huge stack for yourself an auto resolving proves far more efficient when dealing with well defended Planets.
It only pays to use your units, especially your heroes, fully to your tactical advantage on badly defended planets.

I'm not sure how much the A.I. can be altered with when modding, but a more consistent A.I. would be more fun to play against IMHO.
Why not have the ER target my strategic important planets, but with a reasonably Size fleet while it keeps defending its territory?
I mean, why am I the only Player who likes to protect his controlled Planets?
The A.I. will show the same behavior towards each other that they show me.
Does the Empire not care, when it's rival factions take possession of part of their territory?

Anyway, long post.
Thanks again and I hope some of this may find it's way into the next installment?
Cheers guys