Hi there @Hairmac!
Don here from Shopify.
The number of unique discount codes you can create would not be affected by the plan you are using as there are up to 20,000,000 unique discount codes creatable for each store, regardless of the plan you are using.
Are you still considering getting started with Shopify or have you set up an account here already?
In addition to the info on discounts shared above, you might like to check out the other marketing and promotional tools available via your Shopify admin.
Let me know if you have any questions on this info or anything else Shopify-related!