Find a trust-worthy independant mechanic,tell him your story, and pay him $100-$200 for a thorough inspection, watching for failure-prone items.
That would be the most cost-effective way of addressing your concerns. Auto club membership (I guess it would be "AAA" down in the United States?) and a cell phone are must-haves as well.
BTW, statistics show that cooling system failures are the most common reason for older, "beater" cars being stranded on the side of the highway.