The three month thing is out of date as of January I think; last time I looked they just said do it ASAP. It was because of Class II NI contributions which used to be paid quarterly from when you started self-employment, but now it's paid every January and July. End of the month, so technically you should register by then and pay about a fiver. I don't think you've got anything to worry about though. (For the tax side of it you need to register in time to pay your bill by the end of January.)
If you do the ltd. company thing I don't think it makes much difference to the process whether you've been a sole trader already, so no need to decide right now that that's what you'll be doing.