Step 1: Proficiency training
There are two parts to this. The theoretical part will include the law module (to make sure you understand the law) and then there are the specific proficiencies (handgun/shotgun/manually operated rifle/self loading rifle) that will teach you how to safely handle and use the specific type of firearms. You will write a test at the end that you must pass. This is just to test your knowledge.
The law states that you may only use a handgun or manual shotgun for self defence, so if that is the only thing you are going to use your firearm for, I would recommend to at least get those two. If you think that you might take part in hunting or sport shooting in the future, I would then recommend to do everything and get it done with. The process is slow and can be a bit painful, so its better to do everything at once.
The training will also include a practical part where you will have to hit a target with your chosen type of firearm(or all of them). Don't worry, the training provider will guide you through this and supply the firearm/s.
When all of this is done you will get a training certificate and a statement of results as issued by the accredited SETA which is PFTC (Proffesional Firearms Trainers Council).
Step 2: Apply to be declared competent
You hand in your application for a Competency Certificate (SAPS 517) at your nearest police stations' firearms office. The person who handles this is the Designated Firearms Officer (DFO). He will become your best friend, so don't antagonize him.
He will take your fingerprints and send everything off to the Central Firearms Register (CFR) that will process the application. They do a Criminal Record Check on you and this takes time as they manually scan the fingerprints (this is not CSI!).
This step can take around 3 three months.
Step 3: Buy a firearm and apply for a license
This is not 'murica. You won't be walking away with a gun after you buy it.
When you buy your firearm, the dealer will keep it in his safe until your license is approved and you can produce your license card to said dealer. He will give you the necessary paperwork which should be a SAPS350(b) form as well as the SAPS 271 form. You fill in your personal details and then hand it in to your DFO. He will visit your house to make sure you have the necessary SABS approved safe installed. This then goes to CFR to be processed. This can take anything from 3 months to a year, depending on CFR.
As part of this step you'll have to "motivate" a need for the firearm. There are a lot of people advertising services to write this motivation for you. Tread carefully here as most of them just copy and paste some fluff in there. You can write your own. Be honest. For self defence it helps if you add crime statistics for your area or if you have to travel through dodgy areas. Just remember to give proof of everything you say. If you say that crime is bad in your area, add stats and even newspaper clippings. Strictly speaking this shouldn't be necessary, but CFR is full of crap and they make "rules" up as they go along.
Step 4: You are now (hopefully) licensed.
After your application is approved, you can collect your license card and then off to the gunshop to pick up your firearm.
Usually Step 2 and Step 3 can be handed in together. Both your applications will move together to CFR. Your firearms license will at some stage stop and wait until your competency is approved. As soon as its approved the license approval goes much quicker. My competency and license app took just under 4 calendar months (three for competency, 1 for license).
Some DFO's however will not accept both applications at the same time and then these steps happens one after another and the process will take a minimum of 6 months if you are lucky.
Carrying a firearm for self defence is a great responsibility and it is a lifestyle choice. Don't buy it and leave it in a safe, as there will never be enough time to run and get it. Carry it with you (concealed, to be safe no one should know you carry) and practice regularly. There are some nice clubs down in Cape Town.
For forms and info you can visit the SAPS Firearms, Liquor and Seconds Hands Goods (FLASH) website here :
http://www.saps.gov.za/services/flash/firearms.php
Even if you are not planning on joining them, the National Shooting Association has some excellent info:
http://www.natshoot.co.za/page/firearms-licensing
If anything is unclear, drop me a PM and I'll try and sort you out.
Regarding your firearm, I can also point out what are decent choices. Because in South Africa we are limited to what is available and what support is available, some brands are better choices. This is especially true for spare part availability. This is a mechanical object and sometimes stuff breaks on mechanical objects.