If you plan to start your own blog, and generate money (monetize) from it then I strongly recommend to go for a paid webhost, because then you have the ownership of the site. You have to have a domain and a webhost to have a functioning website.

At the moment the cheapest webhost which supports wordpress is namecheap. You can buy both domain, and host from them at a cheap price. Contact them through here support@namecheap.com. They will help you. If you couldn’t get a proper response check their website. or search in Google namecheap webhost. Try the cheapest one first, and move up when you have a good traffic later.
If you don’t plan to earn money then use wordpress.com platform.