You asked some very good questions, however, there are no right or wrong answers. The sites you mentioned i.e. google, ebay, etc. are prime examples of "something new and useful being created at the right time" and with a bit of luck and ingenuity and originality, have become successful.
By "initial capital" for a website, I am guessing that you mean hiring a professional web designer - well, again, that depends on what sort of site you want, what business you intend to advertise; after all, a website is "advertising" and will be your "cyberspace store front". A website designer will design a site for you based on information you provide. If they are reasonably proficient and creative at what they do, they will also include SEO within the content that you provide them, or, you can have him/her outsource the content to a professional copywriter who can write your content for you with SEO upper most in mind. Other things to take into consideration, depending on the business you're in, is how many pages, what do you want your website to accomplish, will you be selling products directly from your site or as an affiliate for other sites, will it be an informational website where you sell "information" such as Ebooks, will you be providing and selling a service, does your product or service have boundaries such as a regional location, etc.
As you can see, the possibilities are endless and creativity has no boundaries. Your site will be as good as the imagination that created it - however, know that websites are never, or rarely "finished" since it's a constant 'work in progresss'. Yahoo and Ebay (as prime examples) are forever changing and updating content. A website can be designed in as little as a few weeks to several months - there are many facets of webdesign to consider, and one of them would be your allowable budget to accomplish this. Some designers can do a 5-page website for as little as a few hundred dollars, while others, depending on what's involved, will charge upwards of a few thousand dollars. It's sort of like asking "how much is a car?" Do you want a Hyandai or a Mercedes?
Before you decide to hire a website designer, you really need to do your homework and determine what your interests are, what business you would like to get into, and how you want to portray it to the outside world. Of course, once you find a web designer, you can always brainstorm over your ideas which inevitably will cause a chain reaction to more ideas.
Then, once you have a website, of course, you're going to need a domain name and a place to "host" your site, so there will be ongoing fees each month/year to consider. But these things are needed for a website no matter what. Another consideration is whether or not you will be doing your own updates, or will you be hiring your designer to make them.
One thing I'd like to point out also is that if you take your business serious and want others to take it serious, do not get one of those "free" websites - they are too volatile and "temporary" and rarely taken seriously as a bonafide business.
I hope I've helped a bit with this information, and good luck with whatever business you decide.
Diane
http://www.distinctwebsitedesigns.com/