I've used the Sharpies and the paint pens and a few other things that placed some kind of ink or paint on the surface. Got fussed at the first gallery I had my stuff in, but assured that the best in the business signed their work the same way. When I got my work back from her, my signatures were faded even though they were under finish. Made me a bit agrivated.
I then tried an engraving burr in a Drimel tool. So much better. Only problem was that the rotating burr would try to grab the grain from time to time and would go off my intended line. It was obvious that it was going to be better than the pen, but still looked bad. Why? Because of the spinning burr going off line, but also because of my poor hand writing. I used a laptop in college and master's programs because I couldn't even read my own notes. Not good.
I was looking through a HF catalog one day when I ran across an engraver with a reciprocating tip on sale for $5.00, I think. I thought that I could give it a try since I'd heard that others were now using them. Besides, I've wasted a lot more than $5.00 of other turning stuff that I'll never use again. Why not. Long story short, it is the only way I'll sign another turning. Before or after the first coat of finish really depends on the wood. Hard woods don't need that first coat, while softer woods like cotton wood do. I would suggest using a pencil to put it on the piece and then use the engraver to go over what you did with the pencil to make it perminent. You can then either cover it with finish of choice or some kind of colored wax. Shoe polish works wonders.