Rosemary likes dryish soil. I'm not sure about basil because I've only ever had it die on me. Rosemary likes to be with lavender, though, and they both like sun. That would be a beautiful combination in a container.

I rarely have any luck getting seed-started plants to live, but I've had okay luck with transplants, since they're past the 'infancy' stage and are a little hardier.

Be sure to drill some holes in the bottom of your tub for drainage, and something underneath to catch whatever water drips out. You can put a coffee filter over the holes so the soil doesn't leak out.