I have a website that I use for my class, so I mostly use it to post links, assignments, news, etc. I use namecheap.com to register the domain and moonfruit.com for hosting and the web software. Total for both services is under US$50 a year, and there are no ads. Designing/developing the site is click and drag, easy to customize and I've been happy. The customer service is really good too, and I did use it a bit when I first started to develop my site.
I should also point out that I have absolutely no programming or design experience and was able to get the thing set up and looking (IMHO) pretty decent for not much money and not much time. A few of my friends with small businesses have used the namecheap/moonfruit combination and have all been very happy too.
If you're interested in the results, shoot me a PM and I'll send you the URL for my site.
I don't think that you will be able to buy a brand new computer at Dell or anybody like that right now that won't be capable of creating Flash files. Just don't skimp on the RAM and you should be fine.