For your needs, the cheapest liner would be to buy a used billboard sign tarp. Probably one tarp would be all you need and you could cut the short way and adhere two pieces side by side to cover the bottom and sides and even have extra.

It is simple to attach to pieces using standard PVC pipe primer and glue.

The tarps are freely available on ebay and very cheap. You have to be a little cautious when wheeling loads of dirt or gravel on it to not puncture it but they are pretty tough. A tiny split can easily be patched with additional sign tarp and glue.

There is a thread about this where a much larger pond was lined this way and it worked really well (and is still holding).