Sharepoint - What's the best way to move a list from one site to another?

I used the stsadm extensions to be able to import and export lists and libraries.

You have already tried the best way, Save as Template and add it to the New Site. And to make the Look Up field work refer to this article that provides an alternate to do it.

Also one another way if wanted to do is to Create a List Template and Deploy it as a Feature using WSP solution, but if you are going to use this List only Once then you don't need to create a List Template. One Another item to note in the List Template is you will have to Hand code the XML with the Data contained in the list. Here is a nice article on how to create a List Template.