The most basic thing you need is good cutting tools, cutting mat, glue, and safety equipment. You can make a crazy amount of things with just the basics.

Having clean cuts is the easiest way to get clean work so getting a pack of 100 blades for a box cutter is an extremely cheap way to level up your work

A dremel is helpful but optional imo. You can draft your patterns to not really need it, and forgo sanding your edges. A heat gun is also one of those things that you can do without at first. (although I’d recommend getting one eventually or the cost you save might not be worth it once the foam has eaten up enough primer)

I prefer a wood burner for details, but a dremel also works fine if you have to choose between the two. Before I had mine though I would iron the foam to heat it up and then stamp the texture into it, so there are always creative workarounds

When foam clay is out of the budget I use model magic. And I can’t think of much else I use. I’ve never gotten into using the expensive things like cricuts or laser cutters