How to make my STORE page more visually appealing with listed products

HI,

I wish to know the best way to go about having my STORE page display mini-product listings in their separate product categories (with thumbnail images of the products) instead of the default as below:

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Welcome to our online store! Feel free to browse around:

Products
Shopping Cart
Order Status

Check out our most popular products:

No Products

Browse by category:

Categories
Rifles
Impact Vests
Bazookas

Browse by tag:
big gun
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*Also, can I change STORE to be/read "SHOP" instead?

Thank you for your help!