For a case of single-account use like this, you're totally fine using the API to programmatically follow. Most of the terms around automated following are clarified here:
http://support.twitter.com/entries/76915-automation-rules-and-best-practices with some more general information on the limits of following here:
http://support.twitter.com/articles/68916-following-rules-and-best-practices
Avoid follow-churn: don't follow then unfollow, then refollow. Keep your following rate reasonable -- though you're programmatically following you should still throttle your actions to a polite rate, especially if you're planning on a larger number of follow actions.
Finally, make sure you're using an account with a bio and a picture, maybe even some tweets. A generic looking account that follows a bunch of users but has no followers or tweets or identity itself is likely to be reported as spam.