For a foam cutter, GT2 belts are the usual winner: cheap, fast, low friction, no lead-screw whip, and the near-zero cutting force means belt stretch is a non-issue. Use 6 mm GT2 with 20-tooth pulleys and idlers, and tension them firmly.
Leadscrews (or ball screws) give lovely rigidity and resolution but are slower, pricier, and overkill when the wire pushes through foam with almost no resistance. Plain threaded rod (M8) with nuts is the budget option — it works but is slow, prone to backlash and wobble, and noisy. Most good DIY foam cutters end up on belts; save screws for machines that actually fight their material.
Leadscrews (or ball screws) give lovely rigidity and resolution but are slower, pricier, and overkill when the wire pushes through foam with almost no resistance. Plain threaded rod (M8) with nuts is the budget option — it works but is slow, prone to backlash and wobble, and noisy. Most good DIY foam cutters end up on belts; save screws for machines that actually fight their material.