There are so many benefits to owning your own domain name. You have a lot more customization options and you can sell ads and make more money with a self hosted site. Having a wordpress hosted site does not help you gain traffic because people still have to know about your blog to find you or you have to be found via Google or whatever search engine they are using. If you want to take advantage of being able to be found via wordpress, you can install jetpack on your self hosted site as long as you still use the wordpress platform, and have wordpress only followers.
There are some disadvantages as well. You have to do your own maintaining of the site. This means you have to worry about the security of your site to a point, if your site is down you have to fix it or have your hosting service help you fix it. There is also a cost involved.
You really have to figure out what works for you. If you just want a way to share your work with others, then a free site through wordpress would work, but you mentioned you wanted to make a career out of it, so I think a self hosted site would be the best option for you, or at least change to a self hosted site sometime in the future (though this can be a long process and is often easier to just start with a self hosted site).