Second Bink re. having a tax account and a good accountant. Most decent accountants will have an initial meeting with you free of charge, and it's surprising how quickly you can tell whether you'd see eye to eye with them. Accountancy is not a DIY job, imo. You also need to see a financial advisor wrt different types of insurance you might need.
I charge an hourly rate, but most of my work comes from public funds, so rates are laid down. For private client work I charge one and a half times the public sector fee. Occasionally people want work done so urgently that it will require me to stay up all night, in which case I charge double the normal rate. My quote states v. clearly that it is an estimate based on what the client has told me, and that I cannot guarantee the fee or the delivery date until I've had a chance to evaluate the work for myself. If it becomes clear that it was more complicated than I had been led to believe, I phone them up and explain.
Cash flow is a bugbear, so second bink's other advice about having a range of clients. I have occasionally done a great deal of work for one client and v. little else that particular month. If the client is then slow to pay, it causes problems. Invoicing £6000 in fees in a month looks great on a spreadsheet, but is worth precisely nothing until it hits your bank account. Cash in the bank is the only thing that counts. I aim to have 10% of my average annual turnover in the bank at all times, and I get v. twitchy if it drops below that.
Payments: My payment terms are 30 days from the invoice date. I work for a range of public and private sector clients -- the public sector ones tend to pay quite reliably within an average of about 6 weeks, depending what stage in their monthly cheque run my invoice hits the right person's desk. Serious delays only usually occur when eg. someone has moved jobs or paperwork gets lost in the system.
Private sector clients (mine are mainly solicitors) can be wonderful (you get cheque by return of post) or terrible (letters are ignored and no-one returns your calls). I'm never quite sure whether they're bent or just incompetent, but for my purposes it doesn't really matter. I have three fairly standard letters that I send out: first goes out about 6-8 weeks after the invoice and says "Further to my invoice blah blah, we do not appear to have received payment, blah blah, I would draw your attention to my payment terms blah blah, please make settlement as soon as possible." The second is slightly tetchier, usually including the phrase "to avoid the need for further action blah blah". The third says something along the lines of "unless I receive payment in full within 14 days I shall have no other option but to take legal action in the county court blah blah". I actually wait 28 days, then I sue. V. easy, you can do it online. As long as all your paperwork is correct virtually everybody then pays up. I have to do that on average about twice per year.
For private individuals I have occasionally demanded (and got) payment up front. I used to be v. wussy and British about asking for payment, but have become more militant with experience, on the basis that they've commissioned the work, I've carried out the work, so they can darn well pay for it.
I dithered for ages before becoming self-employed, thinking that the admin and finance would be a nightmare. But it hasn't been, and I've never looked back for a moment.
Good luck!