Short vowels are more common in English than long vowels. However, short vowels are often more challenging for English learners because they are often unfamiliar with these sounds. If a student is from a European language family such as Spanish or French, I recommend beginning by teaching short vowels before long vowels because of the first language interference. As an adult ESL instructor, I introduce one short vowel per week. For younger English learners, a longer period may be more appropriate.
If a teacher applies the principle of teaching from what is known to what is unknown, they would teach short vowels in a nontraditional order. Most ESOL teachers would automatically begin with Short A and proceed alphabetically. However there are two reasons why I would recommend Short A be taught last. First the American Short A sound is an uncommon sound among world languages. It often difficult to hear and learn, so many English learners struggle to produce this weird sound. Secondly, many students who come to the U.S. have learned British English and use the British Short A. This interferes with learning the American Short A sound. I would recommend the opposite order for teaching short vowels. Begin with Short U and end with Short A. Short U is a very common sound for native English speakers. They use it when they think, "Um," and when they are disgusted, "Ugh!".
When teaching any new sound using visuals is extremely helpful. English learners often connect the sound with the object shown and this aids the learning process. Pictures combined with essential English words relevant to the students' lives, is a highly effective method of teaching all sounds. Vowels, are more challenging because very few essential English words begin with vowels.
As soon as students grasp the short vowels, I recommend teaching closed syllables which end with a consonant/s and contain a short vowel. This is their first step to learning about syllables.