Yes, please register your business with the State Comptroller's office (see http://www.window.state.tx.us/taxes/ and look for the link "Sales Tax Permit Application". It is free (as far as I remember) to get the permit. You just need it to run a business in Texas. As far as I know, your tax id is your Social number, though I seem to remember that I received a Texas permit id number. You will use the number to report sales tax. Even services like mine, fixing someone's computer, is taxed!
It's not hard, just keep the paperwork on file. Keep copies of invoices. Keep track of what materials you buy, etc.
As far as starting something online, you could start simple with a web page on google.com or on yahoo.com. Like http://smallbusiness.yahoo.com/ or http://my.yahoo.com/ (tutorials for a personal yahoo web page is at http://help.yahoo.com/tutorials/my2/index.html )
Getting a site to advertise with would be a simple first step. If you are ready to actually sell online, I also suggest looking at www.paypal.com.
Good luck!