You already got a few suggestions. Just a few pointer to help you decide.
Some shop cater to specific group/language, I assume you/your friend would prefer English then that is not a consideration - the previous mention shops all are primarily English. Bans is by far the largest school that operated 3-4 boats everyday, depends your preference, not necessarily a good or bad thing.
Most large school offer "free" room but varies in detail. Ex. Bans offer air-cond dorm or fan twin rooms free, if you want better room you upgrade with a "credit" towards the upgraded room charge - OW students gets 4 nights free.
Typically shops run 2/3 boat trips per day; 2 tank trip in the morning and in the afternoon and a one tank night dive. You want "as many dives as you can" then theoretically you can get 5 dives per day. Students usually get discounted rate if you want additional fun dives.
Most shops do not go to the further sites everyday and charge extra (SW Pinnacle, Sail Rock) Sail Rock in my opinion is best site in KT, suitable for beginners yet enjoyable by advanced, but it is typically a day trip. Check ahead if the shop you choose goes and on which day, how much. If not there are other shops that schedule day trip (2 tank + lunch) you can book separably.
Above mentioned shops are all in Sariee beach/village area. Convenient but more crowded, party area, beautiful sunset; if you look for quieter area look at Chalok, but less F&B choices.
I spent 2-3 months a year in Koh Tao as my winter escape. If you have specific question welcome to ask me.