First a bit of general advice - If you're taking recommendations from people about the quality of the school or dive sites always ask where else (and how much) they've dived. Diving is pretty amazing so people who've only dived one location will tell you it's great when it might compare pretty badly to others. It can be very difficult to find any properly objective ratings for dive locations as sites change over time(generally for the worse - overfishing, over diving, storms, sea warming, increasing pollution and run off from deforestation).
It's very rare to need to pre-book diving - I reckon you're nearly always better just turning up and having a chat to them first (make sure you trust/get on with the instructors). Pre-booking accommodation is becoming a bit more important everywhere. It used to be the done thing to turn up in the morning and find somewhere but the internet now means the best places tend to fill up prebooked in season.
First thing to do re the surgery is to ask the doctor. As others have said I suspect it's 're-injury' they're worried about rather than anything else. Dive equipment is heavy so putting it on/carrying it about it can be easy to strain back/arms/shoulders but a lot of fat, unfit, people dive so it's not that bad. Ignore talk of 22kg weights(!) - in warm water with a thin wetsuit you only need a few kg at most.
Once you're in the water you're effectively weightless so not a problem. If you do have an issue it is possible to put your kit on in the water (if it's calm) which can be a big help.
Check the climate carefully in that part of the world - when it's good on one side of the Thai peninsula it is bad on the other. The weather is better on the west at Christmas - I think little sun on the east then. Check for the other places I mention as well.
Thailand is a wonderful place to visit. IMO it has the best food in the world. It was the first place i've subsequently visited in SE Asia and every other country has disappointed on the food front. I dived off Ko Tao back in the early 90's and wasn't particularly impressed - however, the only other place I'd dived back then was the Barrier Reef and it was rainy season so the best, offshore, sites were not accessible. Ko Tao will have changed a lot (it was shacks on the beach back then) but I hear good things from people who've been recently). The best diving in Thailand is actually off the west coast north of Phuket. That really is "world class" but we got to it on a liveaboard so not sure how accessible it is from shore/for beginners. East side islands remain more developed and package tourists (Ko Lanta's the best of the bunch), West side still attract more backpackers. Ko Tao still least developed of the Samui/Pha Nang/Tao trio.
Indonesia: climate in all the places that follow is good in December. Huge amount of places to dive but the best stuff is the least accessible/developed as far as I can work out. The diving we did off Bali was a bit disappointing. Gili Islands was better and would be a good place to learn. Further east again I hear great things but difficult to get to.
One place I would hugely recommend is Pulau Weh - Indonesia's northernmost tip. Easy to get to now you can fly to Banda Aceh from Kuala Lumpur with Air Asia. Fantastic diving, a great place to learn as the bay has superb diving in <10m of water, very cheap. Disadvantages - food not as good as Thailand, few tourist so no nightlife. Muslim country (though beer readily available to tourists).
The other place that would be great to learn is Caye Caulker, Belize. I was there in Summer so don't know about Nov-Dec. Again, good diving just offshore, great, cheap, super small, super chilled Caribbean island. Incredible diving once you get properly off shore (though it can be a rough trip out). If you have time you can fly cheaply to Cancun and make your way down through Playa Del Carmen (So so diving but the fresh water cave diving is pretty amazing), Tulum (ruins) to Belize City. The bus ride is an experience rather than luxurious but a good one.
Egypt is out at that time of year as the water is too cold. Liveaboard diving there is really good but the coastal towns are nasty or resort hotels.
how easy is to to get to CAmbodia from Thailand? I have no idea on the layout of these countries but that's something I fancy! Do you organise all of this yourself individually before hand, or is it easy enough of a coutnry to turn up and book stuff as you travel around? 
Lead by a Dive Master so the majority of planning etc is taken care of. 
