Waxed thread is definitely the way to go here, and I'd say that consensus is spot on. I'm pretty new to the paramedic gig so I'm not exactly a master modeler yet, but I've been binge-watching some restoration shows and model-building content lately, and the folks who really know their stuff all reach for waxed thread. The wax coating keeps it from fraying and shedding all those annoying little fibers that would get everywhere in your kitchen - honestly nothing worse than finding model thread bits in your food later.
The main thing that'll keep your workspace clean is prepping your materials before you start. Cut all your thread lengths ahead of time, lay them out on a clean surface, and keep your work area contained. I'd suggest throwing down a small cloth or mat under where you're working just to catch any bits that do fall. Fishing line works too if you want something super thin and barely visible, but it can be slippery and harder to manage if you're not used to it. Waxed thread gives you way better grip and control, which honestly matters a lot when you're doing fine detail work - less fumbling around means less mess overall.
One more tip: work in good lighting and maybe do your rigging sessions in shorter bursts rather than marathon sessions. Your eyes and hands get tired, you start making mistakes, and that's when things get messy. Plus honestly after a 12-hour shift at work I'm way too beat to do detailed stuff anyway, so I get why doing this at the kitchen table in chunks just makes more sense.