The number of bachelor's degree programs leading to secondary subject certification is falling regularly. In a school that offers it, it's called A BEd in English Teacher Education (or similar) or a BA in English with 'teacher certification option' such as this one --->>http://english.chass.ncsu.edu/undergraduate.php
The BA in English alone isn't sufficient to become an English teacher - you must have a state approved teacher certification program with it.
The present trend in teacher prep at the secondary level is to get the BA in English and follow that with a post-bac certificate or a Master of Arts in Teaching (MAT) with secondary English certification. example: http://www.stonybrook.edu/spd/graduate/matenglish.html
The reason they are tending toward the MAT is because the teacher certification bachelor's degrees were leaning heavily to five-year degrees anyway. There are employment advantages to having the master's degree instead and especially if it's going to take essentially the same amount of time.
A minor won't be as useful as a teacher as will a second certification area. Adding a certification area doesn't require a whole new degree - it usually only requires a well balanced 30 hours in the subject. The different states have different requirements for adding a subject area to your certificate but it's generally fairly easy once you have a certificate to teach any subject to add another.
What would help most in getting a teaching job? Math or Science. Having additional certification in either would enhance your prospects greatly.
Related to English and an enhancement? Theater (often a part-time position that can be filled by a qualified English teacher), coaching (especially high exposure sports such as football and basketball), media/library, counseling, K-12/K-6 Reading Specialist, and instructional technology.