What kind of script would I use to make a web based browser, so when a user typed a domain name in the text box and presses go, it goes to the url under the text box..

You can do that with javascript (just put the url input into the iframe source).

what sort of thing are you thinking on having on the browser as you maybe able to do it all in php or you may need a php library to make your life easer.

so if you tell us what else you would need then we can point you in the right spot