Cheapest thing is whatever you can scrounge... sometimes you can get used roof tin, it may have some superfluous holes in it but you know what if it leaks a bit *in your run*, so what
Any kind of solid roof, though, be it metal or plastic or plywood or whatever else, is going to need STRONG WELL-ENGINEERED STRUCTURE supporting it. (ie, more scrounging, or buying some lumber).
Your basic problem is that wind wants to lift your roof away, and either the roof gives way (your ruined tarps) or your structure gives way (whole thing goes sailing through the air) unless it is quite strongly built. Also snow wants to squish a roof down, especially wet snow or snow-then-rain, and again, if it is nto built *really* strongly, either the roof gives way or the supports give way.
Unless you're prepared to really Build the support system, sometimes it can be *better* to lose tarps than to lose the whole run, you know? Just something to factor into your pondering.
To the extent that the tarp damage is not from very strong winds, just from UV and flapping, you can greatly extend your tarp's lifespan by a) shell out more for UV-stabilized tarps, and/or b) strap it down REALLY WELL ALL OVER ITS SURFACE with ropes or wood that hold it tightly pressed against sturdy wire underneath it. (Although, see previous two paragraphs
). The less it can flap, the less it will rip.
Good luck,
Pat