I'll try to answer in order.The "ideal novice student" has a good-handling, unmodified car with low horsepower. This car allows the student's inevitable errors to be corrected without incident. The car strongly rewards good driving techniques and "punishes" driving errors with slow speed. A high horsepower car hides errors. Messed up the corner? Just squeeze on the power and you'll never know. Plus you'll be passing everyone.
The ideal novice has an open mind, listens well, and follows instructions. Some students have native talent and quickly develop into accomplished drivers. Others (frankly like me) take many hours of seat time to develop their skills.
The ideal novice is interested in learning and polishing driving technique. Speeds comes with skill, rather than with just "pushing harder" like you hear the crew telling the F1 drivers.
As an instructor, we have a series of priorities, which are, in order: Keep people safe, then keep car from being damaged, then teach good driving, then have fun.
A novice in a fast car can be a recipe for disaster. While the novice may be driving a lovely line, with nice smooth inputs, something may go wrong, such as oversteer, which an experienced driver could correct but a novice with limited experience, may simply not have the reflexes to save. Such a car/driver may go through many schools and never have anything go wrong, eventually developing good skills. Or they may squeeze on a ton of power, the rear may step out, they may lift off the throttle in fear, and loop-tee-loop there they go, perhaps into something stationary.
Generally the driving school line is a fast way around the track, with some compromises to enhance safety. It is not exactly the same as the line that an instructor might drive, nor is it the same as a racer may drive (because the racer may well be defending his/her position, or attacking the car in front).
Until a novice can drive the school line fairly repeatably, it is asking too much of the student to also have advanced braking techniques, such as trail braking or even threshold braking.
Vision, however, is very important for novices. Assuming that the novice knows roughly where the track goes, but is having trouble repeatably putting the car in the right place, often learning to look ahead will naturally allow the hands and feet to guide the car there. Substantial practice is still needed, though, to know how much steering input is needed, when it should be applied, how fast it should be applied. And the same for the brake and throttle.
Hand position is helpful. I will mention the 9-and-3 driving position to a novice, but often there are "bigger fish to fry". You can't learn everything at once, so part of instructing is setting priorities.
We try to work with instructors so that they teach the same (or similar) driving lines. Feel free to comment about the difference, and maybe I can offer some prospective. Many corners have different lines which are very close in speed and may suit one particular type of car or another. I may also fine-tune what I teach to suit the student's car and/or tendencies. For example, a straight-line approach to the cone at T9 allows for straight-line braking, and I would prefer that to any other line for your car.
The goal is most definitely to develop skills to the point where you can enjoy practicing them (eventually solo without an instructor) in a safe environment. Everyone is different, but it took me several years of attending as many events as I could before I solo'd, and a few years beyond that before I started instructing. If you have only 3 days of experience, you should not expect to drive like someone who has been doing it for years, unless you have some incredible native talent (like, say, Paul Newman).
Don't get discouraged. I was speaking with a friend who is a club racer in a lower horsepower car. We used to be pretty comparable in terms of speed, given my higher horsepower, but street-suspension and heavier car. A couple of years later, he was quite a bit faster. I asked him what miracle had occured. "Massive amounts of seat time" was his reply.
I'm unclear exactly what is frustrating you. If you are being taught very different lines by different instructors, you might express a preference for a different line and see if the instructor is OK with that. For example, there are at least three different entries into T1, and an argument can be made for all of them. The traditional school line is a high entry, tight to the wall. If a student has a strong preference for a low entry, turning toward the pit wall at the 300 marker, braking in a straight line, the turning tight at the apex, I'm usually OK with that, unless I think they will spin on the tight entry (probably due to unintentional trail-braking).
It is also part of a driver's skill set to be able to drive different lines and evaluate them. So learning different lines is not a waste of time.
Assuming you filled out instructor evaluations on your instructor(s), you will receive an evaluation from your instructor on your driving. Our chapter is one of the few in which these evaluations are returned to the student (through the huge effort of the registrars scanning and e-mailing hundreds of image files). This evaluation will probably be very helpful in helping you establish goals for your next event.
I hope this is helpful. I'd be happy to discuss this with you on the phone, if you'd like. Send me an e-mail with your phone number, if you want (dan underscore chadwick at boston dash bmwcca dot org).