I've just recently upgraded and can offer a tiny amount of insight.
My original machine was.... not well suited to Starsector. It could handle vanilla fairly well, but was very restricted when it came to mods.
It was a 4th gen i3, with 4Gb RAM, and a GT730 GPU with 1Gb.
This was almost entirely bottlenecked by the GPU, which could not handle even simple postprocessing without significant slowdown. GraphicsLib had to be entirely disabled for the game to be playable.
Inadequate GPU with an inadequate amount of memory. Still better than trying to run it through the integrated chipset though.
The other restriction being system memory.
4Gb is not really enough. You can only meaningfully allocate 50% of the system resource to Java (up to a maximum of 8 ), and 2Gb is not really enough if you're really keen on adding mods.
I had a hard limit of utilities plus 2 factions before it started to struggle.
New machine is a 9th gen i5, with 16Gb RAM, and a GTX1660 with 6Gb.
This will be bottlenecked by the CPU, and the aforementioned single core restriction. "Will be" because that bottleneck is something I've not found yet.
16Gb RAM is possibly overkill, but that's a personal thing between how much you can afford now vs. probable expansion of software requirements in the future.
8Gb is probably a reasonable baseline for 'right now', and will allow you to allocate 4Gb to Java which is good enough a for pile of mods.
Performance is a vast improvement with no slowdowns noted so far, even with full postprocessing active in a fighter-heavy battle.
Not changed the battle size from default though, so that might be something to look at.
From this experience, I'd guess that for Starsector the GPU is probably the most important bit. Followed by RAM. Then CPU.
I don't know a great deal about the exact mechanics, so it's likely someone who does could offer some more concrete thoughts.
D.R made a very useful/interesting post about system requirements
here.
