The Web Store is designed to integrate with the teams who have applied to your tournament AND have been accepted to participate. This is by design to prevent orders being processed by the general public, family in remote locations and orders that require shipping. There is also no multiple discount, early-bird pricing, coupons, etc. It is a basic pre-order system that allows you to take orders easily on-line and process the product for easy pick up during team registration or on site.
If you require any of the advanced features above, you have the option to set up a full-featured store and redirect your users directly from the store button on the side rail.
Some popular web stores are at Squarespace, Shopify and Square (might be good if you also use Square at your fields)
Many shirt vendors offer a store as part of their screen-printing services. You may want to check with yours.