So, there's a slight discrepancy I've noticed. The backstory mentions travel to another system, but we lack a Jump Engine design, a ship using one, or even the capability to design a Jump Engine (no max jump radius tech).
8,400BP per year, so 67,200 over an 8-year turn. One thing to note is that any PDCs we decide to build will also come out of that budget, though there's nothing stopping us from pausing another project to free up industry to build them. 30% research labs sounds about right, enough for one per year, as does 30% for mines - I would normally suggest building regular rather than automated, but in this case we probably are better off building the automated ones until the worker shortage subsides. If we decide to go down the missile route, we might also want to have 10-15% of our industry building ordnance factories, and depending on our wealth situation another 10-20% on financial centres may be adviseable. The rest can probably go on construction factories.
Research wise, I think the first thing to design is a huge (at least 20HS) active sensor for the sole purpose of sticking on a PDC to moniter Martian ships and provide target aquirement for our ships when near Earth, so they don't have to rely on support from the Hamlet. We could also, if we want, add to that a missile fire control and missiles with similar range. If we go with size 5 missiles and maximum-reduced launchers, we could have a highly capable defence system firing a salvo large enough to overwhealm the NMC's missile defences and with the range to reach Mars for much of the year. (Some testing I did reveals that we could probably design all this for ~4000RPs. Easily doable if we give Stephens most of our labs and a year or two. That was with the 20HS active sensor and a strength 9, 15,000km/s, 126mkm range missile for reference. We might as well add a ship-based launcher to that as well.). If we aim for ~2,400BPs on the PDC we should manage to build two or so by the end of the turn if we put another production order on hold.
The rest of our research points could be spent on various cheap tech upgrades. The next levels of Capacitor recharge rate, Fuel efficiency, and maximum engine power only cost 2,000 RPs each and with our best specialist in that field we might as well snap them up, possibly the next two levels of each even? Expand Civilan Economy could also help, again depending on our wealth situation. If we go with missiles as a main weapon we'll probably want to grab the next few levels of ordnance production and magazine efficiency, along with the next level of missile agility and maybe reload rate. If we're feeling particularly brutal, the first two levels of enhanced radiation warheads are only 3,500RPs and would greatly help if we decide to screw the peace and bombard Mars into submission (after all, we are the evil empire).
If we stick with lasers then capacitor recharge rate and laser wavelength should be our top priority, as well as the next level of beam fire control range. With capacitor recharge rate 4 the 12cm laser firing rate will drop to every 5 seconds, the best in the game. Composite armour will also become more important if we go down this route.
In any case, once the first round of weapons upgrades are done we'll have to decide whether to go for Research Rate or Ion Engines first. I have no preference in that regard.