Proper way to manage multiple variants?

Did some searching but can't seem to find much on my specific question. A lot of threads here explain characteristics but my question is...

If I'm creating a site to sell for example shorts, and the customer selects both a color and size, should those both be characteristics? Is there a way to have the size dropdown simply be a number that is appended to the name of the item on the order form rather than an entirely separate variant of the product? My problem with this is that... if I have 5 colors per pair of shorts and 3 sizes, that's 15 variants per product. First it's not convenient to manage, and second... if I have different images based on color selection, I don't want to have to upload 3 copies of those images just because there are 3 different sizes to choose from.

So, I'm hoping, there's a way to configure a product with multiple color and size choices, without having to hassle with managing size variants but rather just having it be an option that's appended to the order?

Thanks for any help.