Basic auth is just a standard way to send username and password from a client via HTTP to a server. It doesn't define whether to use underlying SSL, or whether this is the first of several calls.
What I want to say: you can decide.
However, REST is meant to be stateless, thus you should rather send it every time you connect to the server, instead of creating some kind of session.
The advantage of basic auth over REST-params is, that the former is part of almost every web-framework (e.g. Java EE, Spring Security). While the latter will add the extra params to all your requests and needing you to check it every time yourself.