Since you are new, it really doesn't matter that you get a top coach at first. You want to learn the basics of
1. Falling safely (as a martial artist, you can, though you may want to practice the sliding falls along with rolling falls, because they are often more gentle on the ice).
2. Balancing on one edge of one foot while gliding forwards and backwards, by shifting all your weigh to be over that balance point with every stroke.
3. Using the edges of your blades (and by extension, feet) to push and pull with those edges
4. Pushing more outwards than back on basic strokes. Don't touch your toe pick to the ice on basic strokes.
5. Keep your back reasonably straight, looking ahead or slightly up, and generally having an attractive posture. The forwards lean that bike racers use is very efficient (though it may eventually give you a sore back), but doesn't meet the artistic standards of figure skating.
6. Keeping things aligned in such a way as to avoid damaging the body.
7. Using your muscles efficiently. A lot of people think they don't have the strength to push and pull sideways against edges - but that is mostly because they are so scared of losing their balance that they tighten all their muscles at once to make themselves stand completely still. That means they use muscles which pull the leg one way at the same time as muscles which pull it the opposite way - and they also tighten the "stabilizing muscles" which try to stop all motion. It takes more strength to stand perfectly still than to do basic skating motions. Once you learn to selectively loosen the muscles that prevent the desired motions, while keeping enough muscle tension elsewhere to maintain good posture and avoid uncontrolled oscillations, the basic skating motions are almost effortless. For many people, this idea of using muscles selectively is very hard to learn, because most people are mostly unaware of what muscles they use. But I bet it will be easy for a martial artist like you, if the movies that show martial artists doing elaborate exercises to gain perfect control of their bodies are anything like reality.
Any figure skater could teach these things, if they understand how to teach to your style of learning. Until you can do these things, there is going to be very little difference between the styles that high and low level coaches teach, and it is a waste of the high level coach's time and your money to use a high level coach.
As for the skates, i realized that they have to fit like gloves, and it is better to give you a little pain on the toes than having room and then getting blisters. I am still recovering from a huge blister. Some other time, i tried some uncomfortably small skates,i was suffering for 2 hours but when i took them off, my feet were ok!
I disagree! Boots need to support your feet, whereas gloves only need to look nice and keep you warm.
Boots shouldn't create pain anywhere. A good fit mostly means uniformly firm pressure almost everywhere. For most people, there are three exceptions:
1. You want lessened pressure around your toes. Your toes are possibly the worst places to squish, because it can create a number of severe medical problems over time.
2. You want no pressure in front of the toes.
3. You want little or no pressure in front of the ankle or behind the ankle - so the boot doesn't cut or press hard against the leg when you point your toes or flex your ankle the opposite way.
Blisters happen when somewhere on the boot is too loose against your foot, and rubs against the skin. Instead of getting a small boot that squishes your toes, get one that is larger - or better yet, one with wider space for the toes - and add tape or moleskin to the boot to fill the voids where it is loose, to try to make everything right. Also, cover the blister with a bandage, so the boot can't rub against your skin there, or it will get worse.
>My feet are not very flat but they don't have the perfect arch
There is no "perfect arch", and unless you have feet that are extreme, there are no "flat feet" or "high arches". But there are shoes and boots which happen to don't fit your particular feet. When people say they have "bad arches", "flat feet" or "high arches" they just mean that most shoes and boots in stores near them don't happen to fit the shapes of their feet. But you can fix that very easily. If the insole is soft and removable (most are), you can put tape or moleskin underneath it so it matches the shape of your feet. If you need more detailed instructions, I can send you a link.