There are a number of ways to promote new products on your site. You could add a 'new' product tag when adding products to your site, and make an automated collection that only includes products with the 'new' tag. Then, maybe once a week, in your Shopify admin you could filter your Products by the 'new' tag and remove the tag from any products that you no longer want to show in the 'New' area (e.g. using the bulk editor).
You can place a 'New Items' link in your shop's main navigation bar, linking to this collection, and even add a drop-down menu under 'New Items' if you want to link to separate automated collections that are based on multiple product-tag conditions, for collections like 'Women's New Items' and 'Men's New Items'.
You can also promote this automated collected by linking to it in other places (e.g. using the Welcome Bar app).
Oh yeah :) - there should be at least a few ways to do that: