My feeling is that a blog is more useful to authors than a website. It's also a good idea to set a day of the week when you commit to writing a blog post so that it's regular.
With a blog you can post a link on Facebook and other places, and people can interact with you. Seeing how you write on the blog also gives them an indication about whether or not they might like your writing style and empathise with your ideas.
You shouldn't be put off blogging if you don't see many people following your blog, because they might read it but not follow, and I know I have people who follow anonymously. You will also find they probably mainly answer your blog posts on Facebook when you post the link from there. So you might not get many comments on your blog, and that doesn't matter.
A website is a much more static affair. It has information and people will go for that, but you can find it's harder to get traffic to a website because it isn't updating as much as a blog. They will also only follow a link to a blog if you've written something that intrigues them, so it's not just about updating regularly.
With a website the information tends to be about the author, and there are so many authors out there trying to ask people to look at their websites and examples of their writing. So you have to tempt them in via a blog. They might then follow the link to your website.
All of these things work together - Facebook and other social networks, a blog, your website and your publisher's website. They should all be interlinked so people get interested by something you say and then follow the links.
We put a detailed author page on our Ward Wood website too, which also links to the author blogs, Facebook and Twitter pages, and websites. Plus we link to any videos and examples of work, and the book sales of course.
I'm not sure how worthwhile it is to invest in a website if you mean you intend to pay a designer. As authors we are constantly being approached by people who want to be hired for this work.
I've never had an author website myself as it has always felt like just one more place to try to attract traffic and the advice I've usually been given is to try to keep everything in one place online if it's possible. It isn't possible so I just try to narrow down the number of places people need to look for my information.
For the same reason I haven't set up book pages or a fan page on Facebook as I try to keep everything in one place - although I need a separate group page for Ward Wood and also for one of the Lumen and Camden Poetry series of events I help with (groups are needed to send invitations).
People who ask to be hired to work on author publicity tend to spend time setting up an author page on Facebook and book fan pages but I'm still to be convinced they actually help. I'm not always convinced hired publicists understand the best use of Facebook for authors.
I'm a fan of Kazuo Ishiguro on Facebook as he's too famous to be able to be on there personally, but I'm not sure fan pages for all authors serve a purpose. People want to follow us on one page - our main page I think.
Of course if you do have a website it will say as much about you as the cover design of your books. Will it be minimalist, with a pared down design that tells the world you're a literary writer? Will it be glossy and full of frills and show you're a commercial writer? Are you a bestselling author with readers who will expect an expensive looking design, or a poet whose readers really don't expect that? Or are you aspiring to be a bestselling author so it helps to look like one? Once you start getting into website design all sorts of factors have to be taken into account.
Readers don't have the same expectations about a blog - they want to see what you have to say, and if you're good at illustrating with artwork and photos then all the better. You need to ask yourself if you need a professionally designed website to reflect who you are as a writer, or is it enough to create what you need using Wordpress?
I don't think a website can hurt unless the design puts you in a category of writing you don't want to be involved in, and neither can a fan page or book page on Facebook - so long as we don't keep asking people to look at them as that just sounds like such a huge number of authors saying 'look at me and my writing' rather than 'I have this post on my blog which might be of interest to you.' It doesn't have to be about books and publishing. You may have something unique about your lifestyle and you can let us into it.
It can feel and look narcissistic to ask people just to come and look at us and our work. To have interaction with people online we have to genuinely be offering something they want and need, and we can do that with a blog. Of course, I also think we're offering something they want and need when we offer our books, but they'll decide for themselves which authors and publishers they like enough and they will buy their books.