Ash here from the Shopify team.
Each Shopify plan allows an unlimited number of products. You can check out the full list of plan features for each plan here on our pricing page. The theme that you use won't impact the number of products you can add, but there are some themes that will be better equipped to hold large inventories than others. Here's a link to a collection in our theme store with themes ideal for larger inventories.
Let me know if you have any further questions!