Congrats!!
I never use anything but barnyard fertilizer on my melons.
Don't use the plastic under your melons as it can hold water and cause rot which is what happens when they are laying on the smooth dirt, if your dirt is big enough clods where it will allow for air flow under the melon it will be fine.
Put some pine needles, hay, yard clippings, or even some small twigs under the melons but don't use anything that will retain or hold excess moisture, such as the plastic.
I noticed yesterday that I have some baby cantaloupe and watermelons ....Yippee!!