I've sometimes earned laughter when I used 一个女人 or 一个男人. Does it have a derogative connotation?
Is it better to use 女的/男的 or 女生/男生? Are there regional differences in the usage?
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男人 and 女人 are used when talking about the relationship between women and men or when talking about specific characteristics of 男人 or 女人. Without knowing your detailed context, my best guess would be that you use them to indicate a serious situation where the generic gender terms should be used, which are 男的 and 女的, or just 男 and 女.
Does it have a derogative connotation?
No, as a native, I'm pretty sure it is perfectly fine to use such an expression. My best guess as to why you've "earned laughter" is that there is something in the context that we're missing. If it is convenient to share the context, I might be able to help you understand the reason better. Contexts can make them derogative.
Is it better to use 女的/男的 or 女生/男生?
They all have their best situations:
Are there regional differences in the usage?
Absolutely, remember Chinese is a group of languages -- there are other words to express the same meaning as well. However, it is out of my knowledge to give a comprehensive overview on how they are used. Edits are welcome, blink blink.