Everything on your list other than the basils should all be easy-care plants, and should take off once they get established. The mints and oregano will need monitoring to not spread too aggressively. I don't do any sort of barrier for mine, I just use my spade in the early spring to limit their natural exuberance. I've had some problems with winter-kill on rosemary, I think it may like winter protection until it is firmly established. I agree with previous posts, baby your new plants at the beginning, water them in well when you plant them out (and keep up with the watering that first year), and hold off on fertilizers. Sounds like you may need to protect them from too much hot sun in your area, something I have no experience with as I live in a temperate region. Perhaps
@Trish will chime in - she has a nice spiral herb garden in Texas and may have some southern advice to offer, particularly to get them established. Best of luck.