Is buying a website business off e-bay a good idea?

No, it would not be a good idea to buy a "business for sale" on Ebay.

You could find a cheap website on ebay but if you do a search, you will see 99% of websites for sale there does not have a good quality. A professional website tells a lot about your business.

I would suggest you to have someone build your own website. Some designers charge a very affordable price. You may consider to check out the following websites
www.onlinebusinessassistant.com
www.websitebroker.com
www.dealabiz.com
ww.dealasite.com

No, unless it's a solid business and has a brick and mortar location that you can check out. The Internet is not a physical place and the sale of a business is not like the sale of a real place business. I could set up a website, claim to have made thousands of dollars a day, sell it to you and you get nothing but a web site. Set up your own web site and do what they are doing. If you want a web store check this out http://manco.fsc2.com , the site, training and support are FREE. It's not a get rich scam, you have to put some effort into it to get something out of it.