Organizing Products Using Categories and Tags

I have an online clothing shop. I am looking for best practices to organize products using categories and tags.

Website is 1923MainStreet.com

Right now I have Women's and Men's categories. But I would like to go to a second level to have e.g. Shirts (and others) under each.

But some shirts are men's only, some are women only and some are unisex.

So under Women's > Shirts I would want it to show you only women's and unisex.

Under Men's > Shirts it would show you only men's and unisex.

So I can't simply tag each of these three kinds of shirts with "shirt" because there would be no way to sub-segment them under men's and women's or both (for the unisex items). Is there some elegant way to do this that I am missing?

I also want to have Collections (like Flower and Garden) that I can show in a summary block. I'm guessing tags would be best for those items (which can span men's and women's).

I am confused and stuck on how to have Women's Shirts showing only the women's and unisex and Mens' Shirts showing only the men's and unisex. Unisex would appear under both.

Is there a way to do this? I'm finding organizing products to be a real challenge in Squarespace.

Thank you for any expertise you may be able to share (even if the answer is that it's not possible in Squarespace).