Sony and cameras
Sony is one of the largest brands in the electronics market in the world, their first camera came out in 1988 but they didn't really take up market space till 1996 when they launched the first of the 'Cyber-shot' series. This series was a hit and based on it Sony cameras held a 20% share of the overall camera market which did eventually drop by around 2005 when DSLRs made waves.
The point & shoot kind
These point and shoot cameras are easy to use for people who don't really understand the technical settings of photography but want good results, which are achievable on auto settings. Also known as fixed lens cameras as there is only one lens that has built-in analog zoom and then digital zoom that is a software function, adding a lot more zoom but generally the digital zoom isn't as clear. With an option to shoot video as well making it a relatively convenient device as you have an all-encompassing camera unit. For a while the files were stored on internal memory later Sony introduced their proprietary Flash Memory based storage 'Memory Stick'. Their current cameras allow for various options though including variations of Memory Stick and SD Cards making it easier to sort your space needs.
DSLRs & mirrorless cameras
In 2006 Sony acquired Konica Minolta and used their technological steps to follow up with a DSLR series called 'Sony α' often transliterated as Sony Alpha. This is a successful series owning about 13% of the DSLR market behind Canon and Nikon. All being Japanese brands a testament to the efficacy of their technical electronics knowledge and production. The Sony Alpha portion of their business also added another interesting camera type called a Mirrorless Camera, meaning there isn't an optical viewfinder so you see a preview directly on the screen instead. These are a lot more compact as the mirror takes up quite a bit of space inside a DSLR. This reduces the shake caused by the mirror flipping when you click after framing a shot with a DSLR, also better for video and overall perform faster as there isn't a moving part inside. The downside being there are fewer accessories and lens options with these Sony cameras and are still not considered as advanced as DSLRs. Perhaps for video though the mirrorless cameras work better as the DSLRs can’t use phase detection with the mirror up while recording video so they have to use the slower, less accurate, contrast-detection focus method. This leads to the familiar blurry look in the middle of a video when the camera starts hunting for the right focus.
Which Sony camera you invest in is a matter of what kind of performance you expect out of your camera and also what you have in mind for how much you want to spend.