Before choosing a blog host, first figure out what your blog needs are most and what do you actually want to achieve through your blog. Depending on these goals and intentions choose a blog host that suits your purpose best. For example, most blogger blog just for personal use and pleasure and therefore are satisfied with the most basic requirements, but if you are looking to use your blog for your business purpose, then your requirements and therefore choice of web hosts will be different.

If you are not comfortable dealing with HTML, encoding and other technical features, opt for blog hosts which are simpler with less technological features. On the other hand if you are an expert blogger and technologically adept too, you can go for blog hosts which offer you great features to fully customize your blog.

I'll add on to what chrismr stated:
You do not actually buy domain names, you are really only leasing them. If you do not renew a domain name then it becomes available for someone else to use.
Once you have registered a domain name you are free to use it for a web site, FTP site, email, etc. But, all you have done is register the name for your use. It does not mean those services are included with the domain name registration.
So, if you want to set up a website you need to have a web-server (i.e. a PC running web server software). You can set up a web-server at home, but you will usually have to pay more and be responsible for keeping the machine updated. It can be a fun learning experience, but if you don't want all the hassle go with a hosting company. In fact you can break up the hosting such as have email hosting in one place, FTP hosting in another, and web hosting in another. You can even have those split up in different places But, usually it's easier to go with one company.
Now, you might be wondering how you can break up the hosting. Well, there is a 3rd component which was not mentioned. DNS hosting. You also need to have a record for your domain name on a DNS server. This tells all the other DNS servers in the world (and they tell all the other computers) how to connect to your "sites".

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