Should I use a not-self-hosted website for both blogging and collecting academic materials?

In academia, an amateurish-looking website can almost be worse than having no website at all. Now "amateurish" here does not mean "made yourself"; it instead refers to sites that use bad design practices (lots of garish colors, ill-chosen animations and transitions, poor design choices that make it hard to find information). However, there is not necessarily a strong link between poor design and web host. So, you can and should decide if the web host makes sense for you.

I know a number of researchers who have their websites that are hosted by sites such as Google Sites, but they do look professional enough to pass muster. On the other hand, the main issues for a web site in academia is that you are able to find the information you need. A bare-bones text-based website (which many people still use) is perfectly acceptable if you can access a researcher's CV, lists of interests and publications, and get contact information.

Wordpress.org gives more flexibility than wordpress.com. However, if you are going it alone, and are learning as you go, you might as well start out with wordpress.com. You can always switch to wordpress.org if and when you get frustrated with the limitations of wordpress.com.

If you're concerned about the unprofessional look that a long wordpress.com url might create, I would say, if you can afford to spend $10/year on a domain name, then by all means, buy yourself a nice, succinct domain name. It will be perfectly compatible with wordpress.com.

Regarding the choice of domain name, if namesurname.com makes you uncomfortable, then choose a name that means something to you. For example, if you are a researcher, you could name your site after your favorite research method. Or you could select some object or concept that intrigues you, and honor it in your domain name. Or if you have a favorite butterfly with an esoteric name, you could name your site after it. And you could incorporate a photograph of it into your theme. Etc., etc.

I don't have an opinion on domain names, but I do think you should be careful about mixing information on your research activities with blog content. At the very least, I think your blog should not be the only place someone can find your papers, CV, research interests, etc. Perhaps you could make your blog as planned, and also put up a bare-bones academic website on your department's server?

I say this because the people who want to read your blog and the people who want to know about your research interests are probably not as overlapping as you'd like them to be, and it's annoying for both groups to have to wade through irrelevant information to get to the content they want.