Hi Stephanie. The American Heart Association (AHA), American Red Cross (ARC), and other organizations offer the CPR (and other related certifications). Whether one is accepted over the other is really dependent upon who (what employer or organization) is requiring the certification of you. You should check with the employer/organization to see if the AHA certification is accepted by them. Generally speaking the AHA and ARC certifications are accepted by most organizations, but again it really is up to the employer/organization.
I hope that this helps.
While we may only need the Adult CPR/AED training to maintain our certs, I recommend everyone take the full CPR/AED/First Aid course for Adult/Child/Infant. These are skills that could save a life anywhere anytime. I am a Red Cross instructor and have taken the American Heart classes as well. Either is fine and both will prepare you for almost any emergency.
But we should all at least mentally go through the steps for performing CPR/AED/First Aid from time to time. I review my manuals every two months unless I teach a CPR class within that time. (I review and prepare for each class unless I just taught a class no more than two weeks prior to my next class.) You don’t need a manikin to practice. A firm bosu works great for compression and you can simulate breaths without the manikin. Just rereading the manual is better than nothing.