Preparing the soil and garden for planting?

I moved into a new house last winter and was delighted to hear it had a huge garden in the backyard. Unfortunately, once the snow melted I was disappointed to find it in awful shape. I have fixed the stones around the edges and removed all the garbage and such but once it got the slightest bit warm it exploded with weeds of every sort. I have almost gotten rid of all the weeds to find that they're is a huge ant problem and the soil isn't very good qaulity anymore. Will mixing in some compost make the soil better?And whats a pesticide free way to get rid of the ants? I'm planning to plant all vegetables so I don't want to use any dangerous chemicals. I want to plant spagetti squash, 8 ball zucchini, 2 types of tomato, red bell pepper, onions, lettuce, and red cabbage if you have any advice becuase I"m a total beginner when it comes to gardening.