When you are starting out with your own blog or website , apart from the content there are many things to consider. For example , are you going for free domains and free hosting or paid domain/hosting and the software that you will build the site/blog on. There are a number of options available for both cases.
To set out , it can be a bit overwhelming especially in the beginning , when I started out , I made a mistake of focusing on too much technicalities and that resulted in lagging behind on content. I will suggest that you start out with a free host and focus on your content first. To do this , the most popular platforms are blogger or free WordPress hosting at wordpress.com. It will give you a ready made platform where you can start creating content straight away . One thing I would advice is to go live out with your domain name , that will help to build a better identity and will preserve your SEO when you are moving to different hosting plan.You can buy cheap domains here.
In the free hosting , as can be expected , there are a number of limitations , like little customization and no plugins for wordpress.com and blogger has very little theme support vis a vis wordpress. Once you have reasonable amount of posts and feel that you should market your blog with some unique twist , it is time to host on your own now, at this point if you are using blogger then it is the best time to switch to WordPress , which gives amazing amount of functionality , mind boggling themes and a great community which is extremely supportive.
In the paid hosting part I am using a small orange as the web host for the last two years and I have never had any major problem with them. Apart from this blog , I have one more site with them . They give very quick replies and also give live dial in support (which I have not required so far). I have not discussed the other options here as I want to only endorse the product which I have used. I have read many articles and testimonials before actually settling for them and I have not regretted one bit. You can have a look at their multiple plans which starts at less than $3 a month.
Now the last thing that is remaining is to transfer the content from your free host to your own host. If you have used free wordpress hosting , then you can use plugin like Duplicator . For moving from blogger you may have look at this. So , to summarize you can start with a free blog/platform with your own domain and when you have done the basic content generation for your site then you can move to run the show on your own.