If it were me, I'd sort of break it down into categories of things I needed to do:

1) containers to use
2) soil mix
3) specifics of growing each item
4) how to grow in containers

Per the containers to use, do you have them already? If not, do you have any idea of what you want? Self-watering, irrigated, or you water yourself? I primarily use Earthboxes because I lived in a condo and didn't have a way to make my own and I had no direct water source - self-watering worked well for me. Sounds like time is a bit of an issue for you, so not sure you can make your own. When you water is part of this decision - will you have time to water multiple times a day? Will you set up an irrigation system? Even if you use self-watering containers, you will have to water some of them at least once a day in the heat of Texas summer.

The soil mix is based on your choice of container. Here is where the organic part may have to be stretched a bit, but it also depends on your definition of organic. There isn't an easy answer and a lot depends on what is most important to you and how intuitive vs science based you are. I like to know how things work, why they work, and then optimize. Many people do not care.

Per how to grow each item, my guess is that you'll just have to do a lot of reading at night when the kids are asleep. There may be a forum specific to some of the things you are growing, but remember, growing is also specific to your area. Tomatoes, for example, may have difficulty setting fruit in Texas in the heat. I don't live there, so can't advise you, but I know they will not set when night time temps are high.

Other things you are growing do better in cool temps, such as broccoli, lettuce, and spinach. You've missed the spring planting season, I imagine, but can plant these in the fall.

Per this, I'd immediately make a chart of all the things you want to grow and do some quick research regarding when they grow best - either specific to your area or regarding temperature.

How to grow in containers should come before what container to use or what soil mix to use, though I put it last. Knowing a bit about this will determine the type of container you use and the soil mix you choose. That's where this forum can probably be of most help. If you understand a bit about the properties of container soil and then add to it the characteristics of your area, then you can make some intelligent decisions regarding what containers and soil to use.

Not sure that I helped much in terms of specific answers, but you have so many things at once that maybe breaking it down a bit will help focus you and help you know what to ask and where to ask it.

I think Lathyrus is right on the money. You're best bet will be gathering a little "container growing basics" knowledge before you begin such a large undertaking. You'll also want to have some information on what grows best in your specific climate/environment.

It's true that you may have to compromise a little bit on the "organic" portion of your undertaking, but that does, indeed, greatly depend on your definition of organic. The first factual bit of information you need to know is that growing in containers differs greatly from growing in the ground. Because the two environments differ so much, it's best to save the wholly organic methods for the garden, and compromise a bit for growing in pots. This pertains mostly to the medium you choose, and the fertilizer program you choose.

I would suggest reading the linked article as a starting point. It will give you the basics you'll need to know about growing in the confined space of containers, and it also covers soil and other suggestions for the health of your proposed vegetable container garden.

Remember... patience is a gardeners best friend, and knowledge is truly the key to success.

Happy Growing!

Here is a link that might be useful: Container Soils - Water Movement & Retention 12

First off, I am far from an expert, but I have grown a fair number of edibles in containers. Here is what I would do with these crops coming:

in the ground: all melons, all non-cherry/grape tomato plants.

1 plant per 5 gallon container: peppers, eggplant, yellow squash, zucchini, cucumber, cherry and grape tomatoes. The tomatoes would be better in an even bigger container if possible. The peppers might be OK in slightly smaller containers.

from seed, in large rectangular containers: lettuce, spinach, arugula(at least 8 inches deep), carrots (at least 12 inches deep).

These are cool season crops and you can plant them, but I think you are unlikely to have much success with these because it is so late in the season in Texas: strawberries, lettuce, arugula, carrots, spinach. All except strawberries will probably do well in the fall. I do all of these in containers, but in the spring.

Onions are best planted in cool weather, but I don't know, those might work out.

I've never grown celery or beets, so no advice there, except I think beets are also cool-season.

I group my herbs like this:
from seed in one large container planted every spring: cilantro, dill, basil

in individual pots that I bring in to use during the winter, planted from transplants, but must buy again every 1-3 years: rosemary, chives, parsley, thyme.

Transplants in a stone planter that stays outside all year, planted once several years ago: tarragon, oregano, sage, mint. You could probably bring these 4 in to overwinter, but I'm not sure.

Mint should be in it's own container either above or buried below ground. It can be very invasive.

Hope this helps. I don't know how you are going to prep beds and containers for all these crops, but I sure hope it all works out for you.