I can't think of any edible plant that enjoys solid red clay. Is your garden just a red clay based soil or is it solid sticky clay? Can you shovel it and open it up? Very few plants grow in solid clay but a lot of veggies grow in red clay based garden soil.

The herbs will want dry and gravel-y conditions in full sun. They don't like rich moist soil - well, except for basil and mints.. I would put your oregano and thyme in large pots rather than in the ground if you have clay soil. They need extra drainage and besides the oregano tends to take over the world. Don't expect the thyme to last forever, they tend to flourish and then die so you always have to start new plants or buy some every other year or so and they always do better in pots for me.

The garlic needs the same winter hours that a tulip bulb does in order to grow properly so you should have planted it in the fall. If you don't get it soon I guess you could plant it but I wouldn't expect full sized bulbs this first year. In the fall you would need to replant them after breaking up the bulbs into individual cloves.

Cilantro is also a cool weather herb around here so I wouldn't give it a prime spot in the garden because once it gets hot it will disappear. Collect seeds and start them early next spring.

I would think about planting all the veggies that produce edible roots or tubers in the deepest ammended soil and plant the above ground plants in the less ammended soil. Carrots and taters and such need looser soil to fill out so they might struggle in hard clay.

You can always mound up better soil on top of your clay soil - much easier than digging everything out.

We've got solid red clay. But it used to be part of a tobacco farm, so apparently you can grow that in it? My husband is out breaking it up today, and adding in a bunch of compost that we brought in, as well as some coarse materials. I'm hoping that we can get something decent growing in the amended areas, at least...