This is typically not something you would have to worry about, as the person developing your website will either be a hosting reseller (discussed a little later), or be able to refer you and set you up on a good hosting service. However it is something that is very important and you need to be aware of. The hosting company will basically be in charge of ensuring your website is up and working at all times and accessible on the internet. So if they don’t do their job right, no one will be able to see and use your website (so you can see how important they are). A very good host will agree to a certain SLA (service level agreement), which will basically just detail what they commit to offering you. The most important aspect of this SLA is the downtime they commit to, as you will want this to be as low as possible.
The other important aspect of the host is that they protect your website and prevent people hacking it and destroying it. These malicious parties look for vulnerabilities in a hosting providers server to exploit in order to gain access to your website and make changes to it. Not all hacking can be prevented, however if your website does get hacked, you need to ensure the hosting company makes daily backups, so that your website can be restored back to its original ASAP.
In South Africa there are quite a few hosting providers, and so you have plenty of choices. Quite a few of them will actually be resellers, which means that they are just reselling another hosting providers services. There is nothing wrong with working through a reseller, just ensure you know who the person to contact is, if something goes wrong.
The price you can expect to pay will vary widely depending on a range of factors, such as: the actual hosting provider, the size of your website, the amount of visitors your website receives, how many database your website has, how many email addresses you would like on that domain etc. However for a small website, with a small number of visitors you should expect to pay around R99, and then this would go up depending on how those various factors change, all the way to a few hundred per month.