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'd try a freezer safe zip lock bag. Try to get as much of the air out as you possibly can as even the air moisture in the bag itself could be an issue if it condenses in/on the drive. You might even try the fridge first.