What should i do if i wanted to dig up a pond in my back yard. Is there a way i could keep the water clean without a filter?

Honestly with no running water it will go stagnant. Natural filtration is possiable but not just by digging a hole in the ground. You can have a natural system, but you will need pumps to circulate the water. A subpump will do.

Remember however, if you over stock pond fish that is 1" of fish for every square foot of surface water your fish will not last too long.
There are so many things to think about and yes you can have your pond in direct sun light, lakes ponds and rivers are in direct sun.

There will be more maintenance with a no filter pond, more vegitation requirements and YOU MUST MOVE THE WATER. With no movement in the water the fish cannot have any dissolved oxygen. This is the oxygen they breath.

Break down and spend the 150 clams and get a pond filter.