if you have 5 gallon food grade buckes with lids,
food grade tubing and the supplies to brew
(See, Cheeto, you'll fit right in behind the wall.)
As to the original question, you're basically using, at minimum, pots and buckets. My "brew pot" was a five gallon pot I already had. You could use a food-grade bucket for a primary and not worry about a secondary. But the bottling bucket would be the toughest to do without because you have to transfer the beer to the bottles somehow. I guess a sanitized funnel and sanitized large measuring cup (which, I would think, would work faster than a ladle) would be doable but a pain. Reuse empty soda bottles and you don't need a bottle capper, though you'll have to keep them out of the light (doable).
A minimum kit would be bottling bucket, a primary fermenter (plastic bucket) with lid, and an airlock. At a guess, under twenty-five bucks. Sanitize with bleach,
save soda bottles, it could work.
[edit: I assume you're talking about a hardware kit; you'll still need the ingredients to make the beer.]
[edit2: oh, and welcome to the forums here at HBT]