TL;DR Getting a .co.zw domain is easy and cheap. Starting and running a website depends on your needs, budget and projected income. Without knowing exactly what they are, we can only try to give you some guidelines to kick-start your research.
As you already seem to know, you will need a domain name. You can get the .co.zw that you want online from https://www.name.co.zw
You will also need to:
1. have the website developed. You can do it yourself, if you know how, or find a web developer who can do it for you. Prices vary a lot depending on your requirements and the developers themselves. It can be anything from $20 to thousands of dollars,
2. have the website hosted. Price ranges here vary a lot too depending on the hosting company, package features as well as the type of hosting that you want. Basically there is shared hosting, VPS hosting, dedicated server hosting, co-location hosting and cloud hosting. It doesn't make any sense to suggest which would be better for you without knowing exactly what your needs are.
3. have the website maintained. This is the run part of your question. I'm glad to see that you have thought about this. A lot of people just setup a website and forget about it. That's a shame because this is arguably the most important step in making your website a success. The software that runs the website needs to be kept upto date. The design and content needs to be kept fresh and current. And most importantly, your website needs to be marketed well. Again, it would be silly to suggest what your costs here would be. In any case, when you get to this stage, it makes more sense to talk your about your budget and how best you can spend it to maximise your return on investment.
If you have a very small budget, don't let all this discourage you. Websites make it extremely easy to start small and work your way up.
Full disclosure: I work for Web Enchanter, the company that runs name.co.zw