I've created a template for a client brochure with all its style sheets separated into folders named sub-heads, body copy etc – there's a list of 13 folders (bit obsessive, I know). When pasting(usually from a client Word doc or PDF) into the brochure, it always defaults to the main heading style (and often with a character style rather than None) rather than a style called 'Body Copy' and doesn't even default to (basic paragraph) as I would expect. It's really annoying and does whether anyone might have an answer to this.
When bringing in a lot of copy in from Word that you want to style on the fly I would recommend using File > Place (like you would with an image), then select, Show Import Options, and use Style Mapping. That way you can pick what Word style maps to which ID style sheet. Word does bring in a LOT of styles so try and clean it up in Word first.
If copy and pasting from Word etc make sure you have selected the style sheet you want in the text box before pasting.
Yes, I should resort to the import text options when copying from a Word file – bad habits! However, I'm transfering documents into a new branding style and often have to copy text from existing PDFs. I'm doing what you suggest, anyway, by selecting the InDesign style sheet before pasting. It does seem odd, though, that it would use a style sheet nested within a folder, 3rd from the top, rather than the default (basic paragraph). It's not even as if it's page 1 – the cover – headline (top of first folder) and the first text in the doc. Strange.