I'm not sure where in zone 7 you are, but this below is a great link for when to plant things out. There are several other resources as well.

Most of what you've got you'll need to buy as transplants and it's too late right now to do the peas, broccoli, cauliflower, garlic, onions (unless you want green), and lettuce. You'll have to wait for fall for those.

FOr the rest, get some graph paper and map it out paying attention to shading issues by putting the taller stuff in the back. You don't seem like you're doing beans or cucumbers so you'll not need a trellis unless you're thinking of trellising the tomatoes, which I've heard mixed results for.

Here is a link that might be useful: UGA planting calendar

You have spring/fall veggies and summer veggies on your list.
Spring: Onion Lettuce Broccoli Cauliflower Carrots Peas Potatoes
Summer: Tomatoes Basil Jalapinos Bell Peppers Corn Zucchini Squash Eggplant Cantaloupe
I don't know: Poblanos Peanuts Cilantro Rosemary
Fall: Green Onion (not bulb) Lettuce Broccoli Cauliflower Carrots Peas Garlic

Here is another planting calendar based on your last frost date (since this can vary so much in zone 7!!) ... http://www.yougrowgirl.com/grow. Click on The Lazy Gardener's Seed Starting Chart. You put in your frost date and it auto calculates planting dates for you.

What it does not give you, however, is last possible dates to start things. In my area, that is April 1 for most spring things, although beets can still be planted up until about April 15 and lettuces until about May 1. Summer stuff can be planted starting about the mid to end of April or May 1 up until about July 1 (some things even thru August 15).

For spacing, check out the FAQ's from this forum.