I'm not a redhead, but like you I go straight to burn. So I don't even bother with a tan. People harass me about being white, but I figure, hey, I won't die of skin cancer (it's rampant in my family), or end up looking orange/streaky with self-tanners!
Just pick a suit that would be a good color on you for a shirt, and don't worry about the lack of a tan. Stay away from anything neon!
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