You can check roofing supply places for EPDM membrane which should be in the $0.50/sq ft range and you save the shipping cost. However this is really hit and miss. Only one place in Phoenix sells it.
Plants can be found all around. Even here in Phoenix I can find Canna, umbrella plants and other sedges, horse tail rush, papyrus, etc., growing in people's yards. Many pond plants do very well in a desert climate because they can store water. These plants are called "pond plants" but vernal pool plants might be more accurate. Many people are happy to give you a clump.
And many plants reproduce really fast. $5 worth of Canna can provide enough for an entire pond if you're willing to wait a couple of years and provide good growing conditions.
I understand that Skippy filters are all the rage on the Internet for backyard pond keepers, has been for years and will be for years. But they are expensive and difficult to make compared to other filters for what you get. I think the complexity is the main attraction for DIY people. However, out side of backyard hobbyists the Skippy is not used. Not by fish growers, or people way into the hobby. As an alternative a trickle tower are super easy to make, super cheap and work way better than a Skippy as a bio filter. A trickle tower can be as simple as a pile of rocks in the corner of the pond. Can't be $10 for liner, rock and hose. Of course they can be a bit more involved, but not much.
Or a stream makes a great filter both for ammonia and killing green water. A 10' stream uses about $50 worth of liner, $5 for pipe, and you can get rocks for the cost of hauling. I don't think there is a better combo filter at any cost, and almost maintenance free. And remember, a stream does not need any slope. You can have a 200' stream in a dead flat yard.
Skimmers are really easy to make too,
instructions, and are basically free. The concrete work doesn't have to be perfect and the only tool needed to make the skimmer door is a pair of scissors. Less than $5 for the concrete.
For saving money building a pond an open mind and willingness to learn will save even more than DIY skills. It will always be more expensive to do all the things people will say you "must have". It's an endless list and grows longer everyday.
The only cost I've never been able to get around is liner and pump. However, the pump, if wanted at all, can be much smaller than most people will recommend. That saves both on the pump and running.