If it were me, I'd probably nail down thin plywood (like that Luaun stuff) and paint the floor with a polyurethane floor paint. That way you can remove that floor easily by just prying up the luaun. You can also glue down cheap sheet vinyl over that luaun. Every "Crazy Eddie's Discount Carpet Barn" has 12 foot wide rolls of old or discontinued sheet vinyls that can be had for cheap.
Alternatively, staple thick polyethylene sheeting down and cover with large pieces of scrap carpet liberated from the dumpsters behind the carpet retailers in your area. Normally when they replace a carpet in someone's home, the cost includes removal of the old carpet. The carpet retailer rents the dumpster behind his store for his installers to dispose of those old carpets in. No one's gonna care if you take those old carpets. Scrap carpets work best on concrete garage floors cuz the carpet is warmer to sit or lay on if you do repairs on your car in the garage, provides good traction even when the floor is wet and dirt like sand ends up deep inside the carpet pile where it's outta sight and outta mind. And, of course, scrap carpet is fast, easy and cheap to replace every coupla years.
If you're willing to spend more for a permanent flooring, consider synthetic rubber flooring. Rubber flooring is commonly used in skating rings and golf "pro shops" where people will be walking on the flooring with spiked shoes or with their skates on. You can put out a lit cigarette on synthetic rubber flooring without harming it. And, it comes in a large tile format so you can replace damaged tiles. And, of course, rubber has excellent traction.
The biggest name in synthetic rubber flooring is Johnsonite at: