There is no hard and fast definition of what constitutes a small, medium or large catalog. There are also no limits on the number of products you can have in Shopify.
In terms of design, I'd say it's very important because it can be much harder for customers to navigate and find what they want on your site if you have a lot of products. Main things to consider:
- Clear navigation/menu structure (possibly needing a mega menu, tiered menu)
- Prominent search box (if you have a lot of products, people are more likely to use site search to find what they want)
- Possibly a collections filter, so customers can filter collections by size, price, color or whatever is relevant for your product types.
Some themes that lend themselves to larger catalogues are; Supply Theme (free), Empire (paid), Warehouse (paid), Turbo (paid)
Other thing about large catalogues is they can be a pain in terms of maintenance, so try and automate as much as possible (automated collections, avoid too many product tags, automated image resizing etc. etc.)
There is an app I use a lot with large catalogue stores called Excelify. Makes some jobs much quicker as can do them in bulk and it's better than the default import/export that Shopify has.
Hope that helps.