Yes gas appliances are safe, granted they are installed by a registered gas installer.
When selecting a gas appliance you need to consult the gas safe appliance list and ensure the appliance you plan to buy is on the safe appliance list. If the appliance appears on the safe appliance list it means that its has undergone testing and is deemed safe by the LPGSASA.
That being said there are always going to be some appliances that are safer than others. Try stick to a well-known brand or something that has a few reviews. Most gas stoves and hobs are relativly all the same in terms of safety as they should all have flame failure devices, there are a few appliances out there that do not come with flame failure devices, these should be avoided with the exception of gas braais/BBQ’s and some commercial equipment.
The safety of an appliance greatly depends on the installation. For example, if an installer installs a gas fireplace in a room without ventilation it can be very dangerous as the gasses from the fireplace can displace the oxygen in the room and cause suffocation. Please do not buy a gas fireplace if you are not willing to install the required ventilation for your own safety.
Another example is installing gas geysers inside a bathroom without venting the exhaust gasses to the outside. This is incredibly dangerous and is easily avoidable by getting a certified gas installer.
You have view the gas safe appliance list here: http://www.lpgasdataportal.co.za/safe-appliance-database/