The important aspect of your gravel specification is that it is fairly uniform and clean. The worst choice would be known as bank run, crusher run, modified, or stone dust (these are all "street names" for the materials, your area may have different descriptions, or even state approved codes like 2A, 2B etc.... in common use) . These gravel products have a lot of fine material in them and are designed to compact in to a solid, nearly impermeable material. Any clean stone from pea to 3/4 will allow a lot of water flow through the material, which is desirable. If you need to top the gravel with clay, then you need a filter fabric, or geo-textile to keep the clay from migrating into the soil. The cheapest DIY source for this material is the weed-block fabric available by the roll in a garden center, or big box store. Just roll it out, over the gravel before you place the clay.
In this configuration, a gravel filled trench topped with clay, you can move exponentially more water that the pipe alone can handle.
I once relocated a high volume spring that we unearthed, a few feet from a new home foundation. I placed a pipe in the bottom of a 2' wide trench, covered it with 2' of loose gravel, then capped with clay. The end of the pipe exited to daylight, well away from the home. It has hundreds of GPM flowing out the pipe AND surrounding stone, continually.