I think Oxford's new series, English for Life, is a great resource for older adults beginning to learn English. In my case, my students hadn't studied or been in any sort of academic environment in years and I found that English for Life taught useful English with simple explanations. Each lesson is only 1 page so students feel that they are progressing from early on.
Natural English is another option...the book's objective is to teach practical, conversational English.
Based on my experience with adult absolute beginners, I advise against New English File. I use the books for other types of classes and it's alright, but I find it to be too ¨academic¨ and less conversation-based for older learners.