It helps to start with a general sense of cool weather crops and warm weather crops.
Cool weather crops include the green leafies, most of the root crops, broccoli, cabbage, peas. They are cold hardy, frost tolerant, but don't like hot weather much. They are generally planted in the garden before the average last frost date. For the ones that are direct seeded in the ground, they say "as soon as the soil can be worked." That means the ground in unfrozen and dried out enough that it is crumbly, not clumpy.
"carrots, lettuce, onion, peppers, tomato, beans, corn, okra, sunflower, rosemary"
So from your list, the carrots, lettuce, onion are cool weather crops. All of them are usually direct seeded in the ground. For you, the time to be planting cool weather stuff is right now (if not sooner!). The onions are slow. I usually plant them in fall to be harvested the following summer. The carrots particularly do not transplant well. The root, which is what you want, tends to get messed up. If you want to keep going with your carrots in the seed starter, here's a thread where one of the mods, applestar, gave instructions about how to transplant them, since it's a bit tricky:
The rest are warm weather crops. The tomatoes and peppers really benefit from being started ahead as you are. The rest can be started ahead or can be just planted in the ground.
How many seedlings of each to keep depends mainly on how much room you have to plant them in and secondarily how much of the crop you want/ can use. I plant 5 tomato plants in one 4' x8' bed. That is way crowded by most people's standards. You certainly wouldn't want to put any more in that amount of space. The five plants is about enough to keep the two of us in tomatoes all season, but not much left over (if you wanted to can tomatoes etc).
Corn does not do well, planted as just a few plants. It needs a little block of corn plants so that they can pollinate each other. As a rough estimate minimum would be a 4 x4' square planted with at least 12 corn plants. Corn can be planted once soil temperature (different from air temperature) is about 60 degrees. Unlike tomatoes which generally keep producing all season, corn matures its crop all at once, 1 -2 ears per plant. If you want to keep some corn coming it helps to do some succession planting - plant one block of corn plants, then two weeks later plant another.
I haven't grown okra and don't know anything about how they produce, but they are large plants, at least the size of tomato plant, but even bushier, i.e 6' tall and 4 - 6' wide. You would want to space your plants about 2' apart in every direction. It likes really warm soil, soil temperature like 75 degrees.
Beans are in between the corn and okra as far as when to plant. There are bush bean varieties and vining varieties. Unless you have bush beans, you will need to give the bean plants some kind of trellis to climb (could be just some strings strung between poles). Beans keep producing for awhile, maybe 20 pods or so, maybe 1/2 pint of beans from a plant (ROUGH estimate, varies a lot on conditions). Plant seeds of bush beans 2 to 4 inches apart in rows at least 18 to 24 inches apart. Plant seeds of pole beans 4 to 6 inches apart in rows 30 to 36 inches apart; or in hills (four to six seeds per hill) 30 inches apart, with 30 inches between rows.
The rosemary is a perennial. That means it is going to stay where you put it. So you don't want to plant it in with all the annual veggies. It needs its own spot. A couple rosemary plants is probably all you need.
I would start by figuring out how much room you have and can prepare the soil for and can take care of (remembering that preparing the soil and planting is only the first step, then you will need to be weeding and watering all summer). Once you know how much room you have, then you can figure out how much of what to plant. Since you are new at this, don't take on too much. You are way better off to have a small garden that you can take good care of and be happy with, than to end up mid-summer with a big weedy, buggy mess that you give up on!
You haven't asked about preparing the soil. That's what you should be thinking about right now. The secret to good plants is good soil. So put some effort into preparing your veggie beds well if you want to be happy with the results!
Hope this helps a little for getting started...