The truth is you don't need any of that first. Really what you need is a client. It is not against the law to offer a service without first registering a business name, creating a website or get a new phone number.
My advice, start looking for a client! While you are doing that yes, a business name is going to come in handy. Do a trade name search for any business names you are thinking of using and then do a domain name search. It does you no good to pick a name and not be able to create a website using it. Once you settle on a name go ahead and register it with your state. You will also want to apply for a business license at that time and buy the domain name.
I own several business and the listed address is my residence. That is where I started them, it was just how it worked out. I have never once in the 15 years that I have been self employed had an issue. If you are concerned about safety or credibility (this one you really don't need to be) get a P.O. Box or many mailbox companies give you a physical address that do not appear to be a rented box.
Ok, we have a business name, we own the domain, we have a business license and we are registered with our state. Now - Do we get a new phone line? This one is up to you. Do you feel it will be a burden to use your existing number? If so, get a new line, otherwise there really is no reason, just remember to answer your phone with your new business name if you don't recognize the number.
Next, we need to start getting your name out there so you can get some clients! Facebook, website, business cards, business groups, flyers...Start getting your name out there!
Once you get a client, I would recommend opening a second bank account in the company's name. Just for tax purposes it will make your life and your CPA's life easier.
Congratulations on the new business and good luck