Just a quick thing to offer to rickairs excellent advice in his post.

Most CFI's I have talked with, including myself, would prefer to NOT teach at an FBO. Couple reasons.

I prefer teaching career orientated pilots because they are much more motivated and self driven than "weekend hobby pilots." They are more likely to study on their own, pay attention to you and be more engaged. Scheduling is also better because they will be coming out more often and willing to adjust their schedule.

Part 61 teaching with weekend pilots is a different world. You tend to teach people who are doing this "on the side" are not always as motivated. They don't see doing homework or assignments as needed. They show up more when they feel like it (regardless of scheduling) and often disappear for weeks on occasion.

I teach at a 141 school associated with a University and I really like certain aspects of it - You are given a set schedule so you know (mostly) what your day/week is like although you will often have to work extra or nights. Also, most of our students are career orientated and are quite motivated. Finally, since it is associated with a University, they care about grades so they have another motivator.