Hey guys, I don't normally read a lot of the threads in here but stumbled into this one.
It really depends a lot on what you're trying to make. Right tool for the right job is an understatement when it comes to working in this scale.
I had access to a full workshop that fabricates the custom trade show displays and environments I design. I had almost every tool I needed there. I used a large industrial table saw, band saw, joiner, planer, edge sander, air disc sander, air brad nailer, cordless drills and a jig saw. I also used hand tools like a Japanese saw and chisels.
If I were starting from scratch the jig saw would be a must. Buy a good solid one without a lot of bells and whistles (like the light). Milwaukee and
Bosch are two brands I like, and Dewalt has gotten better recently. You'll want a really fine blade to cut MDF, and one more coarse for plywood.
They have really small table saws that I've used to make bass wood models like this one:

I was working with smaller pieces of wood on the model above to begin with, so I didn't need to rip down a 4x8 sheet for something the size of the space station.
You could look into an inexpensive bench band saw, but you'll need to learn how to maintain it and will be limited by the width of the gate - the distance from the blade to the blade housing on the table edge.
Stay away from tools like circular saws, you won't get the precision you're looking for and will have a lot of work after the cut to get the edge looking good. Also avoid scroll saws - they're really difficult to work with in a variety of materials and the blade always seems to pop out or break.
Regarding materials, I have no idea how you all have the patience work with foam core. I've used it a lot in the past on study models for work related projects and it certainly has benefits, but also some serious deficits. It's fragile, it warps, it's not structural at scale and it can become expensive fast. Nothing I ever used it on had any shelf life at all, especially when I used hot glue to bond it together.
I chose 1/2" MDF for the station because it didn't have the layered edge that plywood would have. If I had used plywood I would have either used bondo to fill the edges or applied a vinyl tape to hide the irregular surface after painting. I did need to pre-drill to keep the material from splitting, and was careful to set in far enough from the edges when brad nailing to avoid a blow out.
The acrylic was easy to work with because I had the parts milled on a CNC machine. If I had used hand tools there would have been a ton of finish work on the edges.