Display in the home page just a selection. How?

Hi,

You can create a special unpublished category, assign it as second category in the products you want on the home page, and create a new module instance of "hikashop content module" via the Joomla modules manager and select that category as main category of the module.
I'm not sure what you mean by "by price" ?
If you want to display the cheapest products, you can use a hikashop content module on all the products with a "column ordering" on "product_sort_price" and the "column direction" on "ASC".