As a backpacker, I'd say it's possible to travel safely in most countries. Sure at present, Yemen and Syria may not be ideal, but otherwise you're pretty good.
First step is to look up your government's travel advisories for the country. For example, New Zealand does one for us for any region in the world. Take it with a grain of salt, however - remember that they have to warn about everything that may happen, but that doesn't mean it will.
Make sure all your family's vaccinations are up to date, so that at least you don't have to worry as much about disease or health.
I don't personally use travel agents much, aside from on the ground. Once you're there, they're likely cheaper to use as well, but with limited time, it may be easier to use one in your home city. It'll certainly be simpler, and in your language.
Also take note of Wikitravel's warnings about safety there. Again however, this doesn't mean it will happen to you.
Have fun, I'm jealous and also impressed and pleased that a family can still travel to places like Guatemala together :)