Several important items may have been overlooked in your outline:
January - Draw a garden plan indicating what you are going to plant and where. This is necessary because it guide seed and plant purchases. Depending on the orientation of the garden, you don't want tall plants shading shorter plants, etc.
If a new garden, you will need to determine how you are going to water it and with what. Some people use sprinklers, soaker hoses or laser lines.
Realize that you may be planting and harvesting all summer long, although your thoughts for September are appropriate.
In our garden the following vegetables have done extremely well; lettuce (multiple varieties), spinach, carrots, radishes, onions (fantastic!), summer squash, parsley, cilantro, cabbage, turnips, and rutabagas.
Our tomatoes have done well but I start the plants in mid-February and plant them in the garden in mid-May using "walls of water" to protect them from the drying winds and perhaps a late frost. Six plants produce more than an adequate amount of fruit. Four plants could be sufficient for most families.
For two years I tried to grow peppers but my efforts weren't rewarded. I finally decided to build a plastic film covered frame. I planted pepper transplants in the garden and covered them with a mini greenhouse until early July. We now have lots of nice sized bell peppers for home use. Given the price of peppers in most grocery stores, the effort is probably worth it ... especially if one is retired and has the time to putter around.
In a small garden, crops such as peas, beans, corn, potatoes, pumpkins and winter squash don't have a good fit because they consume too much space. I grew peas in our garden one year ... they could be trellised on the garden fence ... but the deer discovered that they were tasty.
Lettuce should be planted every few weeks, and sparingly. How much lettuce can a family eat in a week? A problem I have with later lettuce plantings is that they seem to come up and then disappear. I finally realized that mice consume the late season plantings and have to set mouse traps and pray that I catch the mice before they eat the lettuce seedlings.
My comments regarding lettuce bring up another important point ... how does one protect their garden from voles, mice, rabbits, deer, Bighorn sheep, elk and bear? The latter two animals are the only ones that haven't enjoyed our garden. You obviously know that hail can be expected to occur and the most unappreciated time!
Enough comments for you to digest for the moment.
