Should you have a website if you are not published?
Well, that is a question that I think would depend on your situation.
If you are a writer, and feel you want to put your name out there because you are going to write until someone publishes you, then I'd say "yes" get a website.
Even if it's a cheapy site on that cost a few dollars a year for one little page, why not?
I think it shows you are serious about writing. I think it will be easier if someone does want to search you like most people do today.
I wouldn't spend more money than you can afford, but you know you will need to spend some.
I did a yahoo one page template it cost maybe $3 per year. That's it.... Now the page is plain and simple, but being that I hadn't finished a book yet that is why I went that route. And now, I finished a book and I'm serious about finishing more, I'm paying someone to do a professional one. One that represents who I am, and what I like. (which is fantasy, mysterious, spooky & some romance)...
So it's up to you. But if you are serious then you need to put your name out there. The website is the best place and the cheapest advertising I know other than being on writers groups.
Writers groups are another way to promote yourself for free. I see authors doing it everyday and no one minds if they play by the rules.
Hope this blog helps,
Fantasy on the Rocks!!!