There are about 50 dive schools on Koh Tao, all offering open water courses, so it can be very difficult to make a decision based on websites alone! It really depends where on the island you want to stay. Sairee is the busiest village, with Chalok being the quietest and Mae Haad somewhere in between. Pick a dive school near where you want to be based - makes no sense to travel the length of the island every day.
Most dive centres will offer a choice of PADI or SSI, and some (like ourselves) will offer both. Since you are looking at online training, its worth mentioning that with SSI there is no fee for this, its completely free. You just need to register online and affiliate to your centre of choice. Some dive centres are very large, with large boats carrying up to and upwards of 40-50 divers at a time. Other smaller centres will guarantee small groups and smaller boats giving you more personalised attention.
In terms of finding 'the best' school, this is very subjective. The easiest way to help you make a decision is to check out what other travellers and previous students have thought. Most dive centres are listed and ranked on the Trip Advisor activities list:
Ko Tao Activities - 80 Ko Tao Tours - TripAdvisor
You don't need to book in advance as courses start every day. Just read the reviews, find some dive shops you like (you can even even email them with any specific questions), and once you are there have a look around, visit them, meet the staff and the instructors. Then make your decision.
FYI There is also a Koh Tao specific forum on Trip Advisor where you can do more research and find answers to your questions.
Hope this helps and enjoy your course & stay on Koh Tao.
Happy diving
