Final answer:
The isalpha method is the string method that checks if all characters in a string are alphabetic and the string is at least one character long, returning true if so.
Step-by-step explanation:
The string method from the options provided that returns true if a string contains only alphabetic characters and is at least one character in length is the isalpha method. This method checks if all the characters in a string are alphabetic (A-Z and a-z) and there is at least one character. If these conditions are met, it returns true, otherwise, it returns false. It does not consider any whitespace or punctuation as alphabetic characters, thus those will result in a false return value.
By contrast, the isdigit method checks if all characters are numbers (0-9), and the isnumeric method is slightly broader as it checks for numeric characters, which can include numeric characters from other languages besides just 0-9. These methods are used for different kinds of character validation in strings and are part of the many string methods available in programming languages like Python.