How do I setup a simple line listing on the front?

Yes.
First, if you display all your products one one page, you don't really need categories...
Just create all your products in one category ( you can configure their ordering ). Then, create a listing products menu and go in the hikashop options of the menu. There, you will set the layout type to list, and toggle on the add to cart button.
Then, you will have to edit the file listing_list of the view product via the menu Display->Views and add near the beginning the line: $this->params->set('show_quantity_field',1);
If you want to display the category name, I would recommend to add a custom product field via the menu Display->Custom fields (only in commercial versions) so that for each product, you can select a category via a dropdown and then in the same listing_list file view, you can change the line:
echo $row->product_name;
to:
echo $row->custom_field_column_name.' '. $row->product_name;
in order to display both the category and the name
around those lines, you will be able to really personalize the display to have it like you want.

First, you need to change the number of columns in the hikashop options of your menu so that you only have one column.
Then, you will have to edit the CSS of hikashop to have everything on one row. You can edit it in the config under the tab display. If you could give us the URL of that page, we should be able to give you more precise directions.

Almost: "To access the private area of this site, please log in."

If you edit your post, we don't receive a new notice so if we looked directly to your post when you did it, we don't see your modification, which was the case. We'll look at that now.

You can first remove the display: block; in the CSS code :
span.hikashop_product_price_full {
font-weight: bold;
display: block;
margin-bottom: 5px;
}

and then add the CSS code:
.hikashop_product_stock{ float:right; margin-top: -28px; }
.hikashop_product_name_in_list{ float:left; }

That will make only one line per product