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I use a combination of a 3' x 4' aluminum drip pan, a couple of pieces of cardboard to help slide under the car, and Simple Green to wipe up anything that misses those (my floor is easy to clean).
For the driveway, I'd get some concrete cleaner in a spray bottle - something stronger than Simple Green since the concrete is porous.
I had my concrete guy put charcoal grey coloring in the concrete mix before the driveway to my shop was poured...Looks like aged asphalt but is essentially chemical-proof and can be pressure-washed with no loss of color...Perfect for my situation but YRMV...
I also had a guy at a hot rod shop I used to frequent give me an old advertising banner. Standard vinyl or synthetic poly...it was ideal for catching drips under the old classics. It's the perfect length for under a car. Width fit between the wheels and length extended just beyond both bumpers. So maybe search ebay or amazon for something like that?
Probably the easiest thing. That or a big blanket, then it's at least comfortable to lay on lol.
I use the big Harbor Freight moving blankets. And to your point, much easier on my old bones to lay on. And HF usually has coupons for them now and then so you can get them cheap.
I have a collection of big corrugated cardboard sheets from various items I've acquired over the years (Weber grills, garage cabinets, etc, etc). I always use one of them underneath when I do oil changes on any of my cars.
When I built my ICF Home in I used the TK Bright Kure and Seal Product on the basement slab and also the garage and pad. It penetrates the concrete and seals it with a low luster clear coat, this is a no kidding industrial product, 100 X better than anything from a big box store, protects from oil and solvents. They use this stuff in the Midwest to seal all the concrete used on hog houses.