I've safariied about 10 times, I absolutely love it, You really need to look for a family friendly option as a lot of safari packages won't allow children on them (not surprising when you consider the amount of quiet-and-keep-still you have to do). If you want it organised and with a group try explore family holidays who do great family friendly trips all over the place and they always coincide them with school holidays. Where are you thinking of going? I have safariied in Kenya, Tanzania, South Africa, Mozambique and India, all are totally different experiences. (I'm desperate to do Botswana and Namibia but WDW calls too loud at the mo!)
Personally I'd choose South Africa and do a split stay between The Kruger National park and a private game lodge, like Sabi sands or hippo hollow (if you're feeling generous you can't beat Richard Bransons Ulusaba - its the best!) then you'd have the option of staying for a rest at either Sun City (great fun but very plastic and false - some reckon its like Disney world!!) or flying down to Cape town for the beaches (theres a fabulous one where the penguins are so used to people they'll come and play with you) or fabulous shopping and sightseeing.
Sorry I've rambled on a bit but I can't help it, Its my favourite type of holiday, everyone should try it once, If you need any other info pm me