Botswana is one of the most expensive safari destinations, then Namibia and are not what I would consider to be mid priced, although this term means different things to different people. A luxury camp will be a luxury price and you need to work out what your budget is, as the sky’s the limit price wise - hundreds if not thousands of dollars per night per person.
If you really want to go on a safari, your focus will be on getting out and seeing the animals - early morning drives at 5-6 am for dawn and nighttime rides, so you are likely to be in bed by 9pm. Dinner is served early in safari camps. I have found that you need to be comfortable, but you don’t need luxury, as you don’t have the time to enjoy it.
Is your 8 year old interested in animals and birds enough at that age?
In many locations, the luxury lodges are outside the National Parks and therefore a longer ride to get to the action. The gates to the parks are locked at sunset and if you want to go on night drives, you need to stay inside the park.
Many people head to a country and just add on a few nights on safari (3-4 nights), spending most of the holiday doing something else.
I have been to South Africa and Tanzania on safari. The time of year is key to where you go, but presumably with an 8 year old, you are limited when you can travel? I stayed in Kruger in SA, in September, which is the end of the dry season, when there are fewer water holes, so it’s easier to see the animals. Kruger is good for children, as the wildlife is plentiful and much easier to see than in Etosha in Namibia. I stayed in a campsite in the south of Kruger inside the park in a roundel which was perfectly suitable, but not luxury. We had great wildlife sightings, taking organised early morning and evening drives and then, when the park gates opened, we drove ourselves round.
If staying inside Kruger, you need to book accommodation a year ahead.
Ithala Game Reserve was good for rhino and was much smaller than Kruger, albeit we had few sightings of wildlife compared to Kruger.
I went on an April organised bird watching/ wildlife safari holiday in various locations in Tanzania for 2 weeks to see the wildebeest migration, which can be hit and miss timewise, depending on food availability.
Having spent several weeks on safari in total, I haven’t yet managed to see cheetah, but I have seen elephants, lions, giraffes and leopards. You need lots of patience and luck. The time of year is key, as is budget. Safaris are not cheap, even in “basic” accommodation once you add in park entry fees, morning and evening game drives, food etc. If you are hiring cars, you are going to need 3 cars for a group of your size. You each need a good pair of binoculars.