In from the ground up as IR your main goal is the closest Capital shipyard planet, in name: Bilbringi
You have to expand quickly before the NR could reach you, and you should quickly take a few planets from them too, before they are heavily defended.
The beauty of hard difficulty is that AI gains ten times the amount of credits for capturing a planet than you do, so capture and hold as many as you can.
I played a lot of FTGU as the Remnants, and in my humble opinion, the best conquer line is the following:
Farrfin =>Noquivzor =>BILBRINGI!! =>Champala =>Obroa-Skai =>Borleais
This way you only have 2 fronts planets to defend, while also having a capital shipyard.
From this position you can also rush out, and capture Gravan VII if you feel like you have the necessary forces to do so.
A good advice: Build 2 Hypervelicity gun(HVG from now on) in Obroa-Skai, Borleais and Gravan VII.
At this point you have a solid border, what can be defended.
About the Economy: I know it is very tempting to build troops training or HVGs on Bilbringi, but that is your best paying planet, so build up 2 Tax collection agencies(TCA from now on) there.
In Noquivzor there is only 50 credits income, and you can say it's too low to build TCAs there, but you will need every single creit you can get your hands on, so build up 3 there.
Carida(your starting planet) is important, because first that will be your only place to train ground forces (I know that) but after you will have other planets where you can build ground units on, you should really free up the spaces there for further TCAs. Build the maximum amount of 5 there.
That way (if my calculations are good), you will have 2650 credit/week.
That is enough to hold out.
About spending the credits... NO
I know it is tempting to build up huge fleets, but believe me, some times it is not worth to hold the space against overwhelming enemy superiority. Do not lose your ships. Retreat is a good option sometimes. I suggest to only hold the space above Gravan VII with all your fleet, and defend Borleais only on the ground. It is more than recommended to build an advanced vehicle factory there. IMPORTANT: If you decide not to defend the space above the planet, sell or do NOT even build the HVGs there. They are credits you desperately need.
Collect your credits until you can build the cheaper version of SSDs, your first Soverign class. Bring that with a suitable taskforce to Borleais, and start defending the space there, and start rebuilding/building the HVGs there.
After that, just make sure to collect the credits again until you can build your second Sovereign too, and send it to Gravan VII.
BANG! you have an almost unbreakable front line.
After that, you can save credits again until you have an Executor class, and with that(and a suitable taskforce) you can start conquering. If the NR already took Over ILC-905 J'T'P'Tan, Galantos and Byss start with them, as Byss will be the best chokepoint...
If you could do all this, then you only have to be patient and you will surely win.
GOOD LUCK!