If you would like to offer a quote to your user in the cart you must have a destination address, if this is not a value that is known when the user is adding items to their cart then you will not be able to add this.
When it comes to implementing the shipping quote server behavior if you would like to have the user select a service type you will need to add this to the checkout page. There are snippets in eCart for these select lists. You will need to ensure that the select list is placed inside of the checkout form.
The select list can be added to the page from the snippets, go to Window > Snippets, in here find eCart and expand it then look inside of shipping. In here you should see the UPS entries toward the bottom of the list.
You will then need to add the server behavior on the confirm page. When you add in the server behavior you will use the bindings for the shipping fields from the checkout form. If you added the services select list you can use the lightning bolt icon to select this form element for the service type.