I'm personally a HUGE fan of non-stick shelf liner. It's durable, yet disposable. It can hold up well, but if you want to just throw it out and put down all new liner, it's inexpensive to do so. Unlike tile, it's very easy to cut to any size you want. As for cleaning, I spot clean with organic alcohol-free baby wipes. For a deeper cleaning, I pull it out, spray it down with a water/bleach mixture, then rinse until I can no longer smell bleach. And whenever I feel like it's time to replace it, I just cut a new piece to size and I'm good to go.
As for brand, I recommend Duck brand, which is now labeled as "Easy Liner" and available from Lowes or Walmart. I'd advise against getting any with a print on it. To me, the printed stuff has a chemically/noxious smell to it. I just get a solid color, usually taupe.