Both wordpress.com & WordPress. org are offering it but there is slight variation in maintaining and also some features in it.
When you go with wordpress.com, it will help you start with free service by adding it domain to your blog ( for example urblog.wordpress.com ) which is much like Blogspot blogs. Customizing the blog is easy and all the other features are pretty same. You can add custom domain also but it is paid service they will charge for redirection ( urblog.wordpress.com to urblog.com ), you can buy a domain from them which costs you around $18 per year. For hosting, you need to pay $8 per month or $24 per month which depends on the plan you choose.
In WordPress. org, there is no confusion, you need to buy a custom domain from the big rock, GoDaddy etc ( which can cost you Rs 700 per year, you can start with Rs 125 for the first year and then onwards 700 per year ). Then you need to buy hosting, it can be shared or VPS. Shared hosting usually costs around some 4-7k per year and when it comes to VPS it costs around 60-80$ per year with some heavy technical stuff involved. You have full control over your blog and can tweak with a lot of plugins & themes, unlike wordpress.com where it is restricted.
I would rather suggest you to go with WordPress. org and explore it. You will have control over your blog and with a lot of themes and plugins and customization options.