Is there such a website....?

Question

where you can customize it and set it as your homepage that has a search bar and stuff

Answer 1

Not sure what you mean by customizing  the web site, but yahoo.com has "MY YAHOO" which allows you to set up a web page with just about anything you might want as well as color schemes . And if you use mozilla firefox you can even get custom skins for it as well.

Answer 2

http://www.google.com/firefox?client=fir... not customizeable but good