In high availability mode, if you lose quorum then the primary server becomes unavailable. You can manually restore it, of course, but I sense you want something more automatic.
To maximize availability you should isolate the witness from both the primary and the server such that you are unlikely to lose any two at the same time.
You are better off with a manual fail-over mode than with log shipping. It's easier to administer, fail over is easier, and the secondary will be more up-to-date. With the advent of mirroring, I would only use log-shipping for situations where you want multiple recovery sites. Even then, I'd probably use it in conjuction with mirroring or replication.