Not only do you need a website, you need a professional website done by professional designer. In this day and age not only should you have a website but your customers expect it. Most people search for businesses on Google and Bing and if you don't show up someone else will.
It's not enough just to have a website. It's not a set it and forget it kind of thing, it has to be updated regularly, it must have good quality content and it must be easy to use. You might think you can get away with having your wife, nephew, cousin or secretary make a website for you. This would be a mistake. Designing a website is a skill and not everybody can do it even if they know how to use an HTML editor.
A professional web designer would understand the concepts of designing a professional website, there is more to it than just dragging and dropping images. A professional web designer understands concepts like:
Typography Proper use of white space Design theory how to properly design a user interface. Properly optimizing images Best practices Designing above the fold
and many many more
These are just some of the concepts web designers understand that amateurs just can't and these are the things that lend credibility to your website and make it look professional. If your websites is not professional it won't stand out. It won't help you in the least and your prospective customers will lose interest.
Another point to consider is an amateur web designer probably won't test your website on different browsers. So it looks good in Internet Explorer that doesn't mean it will look good on Firefox, Opera or Safari. And if you website looks bad people will not buy from you.
Not only that but a professional designer will save you time, money and a headache. If there is a certain element of your website that does not look right how are you going to fix it? You will have to wait for the amateur to have time to do it and it will cost you in downtime.
So in closing a professional website is absolutely essential if you want to be in business today.
While it may be possible to get by without a website I really don't recommend it.