Home Vegetable Garden Prep?

I live in SE Idaho. I have probably a 10 X 20 ft garden in my backyard. I've used it for about two years since I've lived here. It's full of all the old foliage from last year. It has always had a layer of mulch paper covering it. I've just used existing holes and made new ones as I've needed them. I'm going to clean it out, rip up the paper, and move the soil around where I plan to plant my veg. I've never done it before but I guess I'll go buy some compost, and incorporate it into those spots along with some fertilizer. I'll be using gr clippings from my lawn as mulch. Am I going about this the right way? I want to make this as simple as possible. I don't want to buy a tiller. Also, I'm a little late on cleaning out the garden. How long until I've added the compost can I plant? What kind of fertilizer and compost should I get? What do I do with the existing mulch (It's like wood chips)? Should I just keep everything how it is? I want to build up hills for the watermelon. How can I do this easily without leaving a big hole in the garden?