1. I need a solid T-shirt.

2. I need a plain T-shirt.
3. I need a solid-color T-shirt.
4. I need a self-color T-shirt.
5. I need a one-color T-shirt.
6. I need a unicolor T-shirt.
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Are they all the same in meaning? Which ones are commonly used?

2, 3, and maybe 6 would be commonly used.

1 would be OK if you wrote/said, "I need a solid-color T-shirt" -- but then, that's #3, isn't it? =)