Should I use Particle.variable() or Particle.publish()?

I would use Publish. Have your webpage subscribe to your events and render the data.

Also, as a free user of the Particle cloud, I only get 250 thousand events per month, so I am guessing that one publish is an event, and one variable request is an event?

A publish is an event. A variable request isn't. At the moment we don't have strict limits on the number of variable requests you can make.

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