You can also use Pick n Pay to check out flight prices.
http://www.pnptravel.co.za/
Once you get a good price then check out the Airline's website to see if you can match or get a better price. I always prefer booking with the airline directly because if there is a **** up then you can sort it out at the airport.
The golden rule is that you don't want a long stop-over, that kills you.
Also remember that Air Asia and Nok Air fly from the old airport in Bangkok so you may have a problem if you want to fly on to Phuket the same day. Contrary to all the suggestions but Bangkok Air is the most expensive airline in Thailand. Air Asia and Nok Air is okay but you have to book well in advance to get good prices. I don't book anything ahead and found that Thai Air offers the best prices with the least hassles if you book a day or two before you fly.
I came back from Thailand yesterday and can not recommend Patong, Phuket if you are travelling with kids. It really is a place just to go to party, the food and restaurants are generally over-priced and there are too many people. The place have really deteriorated the last few years. Rather have a look at Nai Harn or Kata.
A much better place to go to with family is Khao Lak. I stayed at Nang Thong Beach Resort and it was great. Big clean rooms and a great beach.
http://www.nangthong2.com/index.htm The cheapest rooms are perfect at 2000 Baht.
A Similan snorkelling trip is a must do and you can split it in two and sleep on one of the islands in tents, the kids will love it. Just ask for an open ticket. The one day trip costs 1500Bht and the overnight trip costs 2500Bht with an extra fee of 570Bht per tent.
Khao Lak is 75 km's from Phuket Airport and the taxi costs 1500 Bht. There are no mini-buses to Khao Lak.
Bangkok is a great city and if you decide to stay then have a look at Khao San Road or Soi Rambuttri for a place to stay.
You can also visit my website in my sig for more tips although it has not been updated with the new Khao Lak stuff.
Feel free to contact me if you need any further advice.