Hello,
You can set specific rights only on the Survey list you have created. What you need to set is the right to add things to the list.
"The right way to do it" depends on your setup and how you are managing your users. In some cases I have created a custom site group and assigned it with the add rights to only my specific survey list.
the latest thing I did was to allow all authenticated users to access a site (I put them as readers) then I assigned the Add rights for the reader sitegroup only to the survey list.
To assign list specific user rights click on the list you want to modify, chose modify settings and columns, chose change permissons for this list.
Regards,
Thomas