Should I bother to register copyrights and trademarks for my new business?
If those are among your goals, then yes. But if you're bootstrapping to get started, the website text and logo may not be as much of a priority as, say, having the funds to pay for adequate insurance or actual business registration in your state, so that you're not running this kind of business with your personal assets exposed as a sole proprietor.
Website text can always be changed, logos tweaked and tag lines revamped. Each time you make a change to that intellectual property, it requires a new registration.
Sometimes, it's better to see overtime which logo or program really has staying power before you invest in repeated registrations.
Talk to an intellectual property attorney to develop a strategy that best fits your business goals and budget.