My friend ran her own web dev business for many years. She had a website, she incorporated (LLC) and she had a business bank account. She also registered with her local community business organization which eventually helped drive close to 75% of her new business referrals.
She did not use an accountant that I recall. Just used QuickBooks software.
It was definitely not the glamorous life many think it is. Dealing with clients as your sole source of income can be trying and very difficult at times. Collecting payment is not always as easy as you think.
You also will find your fair share of folks that want something for nothing, the world for cheap or you to talk on the phone with them and reply to their email questions for weeks and weeks at no charge.
My advice: Keep up on your accounts payables (invoices) and bill for ALL your time spent on a project, whether it be email or phone or actual coding/design work. Track it in 15 minute increments and document it daily. Talk for 5 minutes on the phone with a client? Did you prepare for the call? Did you take any notes or post-call actions? Bill all your time. Include summaries of your time spent on your invoices. This will help your clients realize how much you are doing for them, and take the sting out of the bill.