Email setup for outgoing mail

My first time setting this up, I found it useful to put end goals way out of mind. There are some great tutorials. Work with the goal of sending an email to yourself from CiviCRM. Pay attention to whether or not your outbound SMTP is authenticated or not and all other steps in that task.

Once you get there, contacts and groups are usually the easiest way to organize outbound messaging.

Karl

The simplest way is to use a service designed for the purpose (e.g. civismtp). But even that isn't very simple. Effective mass mail is inherently difficult, and a moving target. Eric's answer is a good answer to "what's the best way": i.e. it depends. Maybe the correct answer is: 'get someone else to do it for you'. If you're using a hosting service, they're probably the best candidate, otherwise you could look up an expert.

to address your primary question "what's the simplest way to configure civicrm for mass emailing?"

That's a difficult question to answer without a lot of context.

In some ways, the simplest is to use sendmail/postfix/php mail(), if that's setup and running on your server. Many smtp relays you might use put limits on how many messages can be sent, that could get in the way of bulk email. But, using the server's local server adds complexity -- you have to set some DNS records and pay close attention to bounces to make sure your messages are getting through and not being marked as spam by some stupid automated system (yes, google, I'm looking at you).

In some cases, I use the local server; in some I use an smtp relay service like CiviSMTP, sendgrid or mandril. Some organizations have services they are paying for already (like google apps) and use that. I've had problems using organizational outlook accounts in the past, I try to avoid having microsoft in the mix, but I think outlook can now handle the verp separator that civi uses for bounce tracking so maybe it's not as annoying now.

So the right answer depends on the resources and skills you have in the organization. Sorry if that is not a complete answer.