Hi there,
Welcome to CNCZone.
I have got an X1 that I converted to CNC myself - it has been very successful and is definitely recommended. At the moment, I am busy upgrading my machine to ballscrews and I will be adding a high speed spindle in the near future.
Let's start with the mechanical side of the machine. The first thing that you may want to look at, if you don't already have them, is the extended x and y axis kits from somewhere like http://www.littlemachineshop.com/. They give you a lot more travel on both x and y axes and add a little extra rigidity to the machine. Even if you do only want to machine watches, you never know when the extra travel may be needed.
To get started, the standard spindle should be fine, although you will probably find that the standard 2000 RPM becomes a limiting factor after a while, especially if you are using small cutters. There are kits available that will convert your machine to a belt drive, instead of those nasty plastic gears, and will give it a maximum speed of 8000 RPM. http://www.tj-cnc.com/
The standard leadscrews are also fine for a CNC conversion - I would guess that about 98% of people who convert this machine don't bother with ballscrews. I have run my machine for about a year on the standard leadscrews and they are accurate and still have very little backlash (about 0.07mm backlash on the x-axis and less than 0.01mm on the y). There is also a facility on the standard nuts to adjust backlash out. Some good advice with the standard leadscrews though, is to ensure that they are always WELL lubricated. If they start to run dry, the wear rates will become ridiculously high. Also make sure that you have thrust bearings on your screws - angular contact bearings are even better. I am changing to ballscrews for that little bit of added accuracy along with the higher feedrates (that I will never use... ), but they are more of an added little 'extra' than a necessity.
When it comes to the z-axis, you have a choice. You can either CNC the quill giving only about 30mm of working travel, or you can CNC the whole head - meaning that the whole head moves up and down under power. Both have advantages and disadvantages. If you go with the quill only, then the small amount of travel can be a big issue with things like tool changes and trying to clear fixtures. It should however, have slightly better rigidty than CNCing the whole head. If you CNC the whole head, you will have plenty of travel, but as stated, rigidity may be worse than CNCing the quill, as you can't lock the head gibs when you are milling. I CNCed the head and have found that as long as the gibs are kept well adjusted, the rigidty is not much of an issue. In order to CNC my z-axis, I replaced the standard z-axis leadscrew with a 12mm trapezoidal screw. Maybe not entirely necessary, but I think it was worth it. I'm now replacing this with a ballscrew.
When it comes to the electrical side, again there are many options. I used a unipolar Xylotex board (which has since been discontinued) with 180Ncm stepper motors. The performance is very good. With the standard leadscrews, I am getting rapids of 1500 mm/min (or around 60 IPM). The z-axis gets around 400 mm/min (16 IPM), but I am not using any kind of counterweight, which would increase that speed.
When it comes to other electrical accessories, I found that limit and home switches weren't really necessary (but would still be nice to have). I have accidentally hit a hard stop at full speed with no damage or deterioration at all. I will be installing limit switches now with the ballscrews, as I'd hate for the screw to come out of the nut (and probably ruin it in the process). An emergency stop button is always a good idea, although I don't have one (but quite honestly, you really SHOULD have one, and I will be adding one soon).
Although I haven't used one, I would think that a Xylotex kit that comes with motors and power supply would be ideal for this machine. Mechanically, something like a CNCfusion kit should also be very good.
Finally, your actual question. Stainless steel. I have never machined stainless on my mill, however I have machined lots of steel and cast iron. I can tell you that some of the steel that I have machined on my mill was A LOT harder to turn on a lathe than 303 stainless was, so I would imagine that if you kept to something like 303 stainless steel, you should be just fine. You obviously can't take huge cuts with fast feedrates, but with CNC it's not a big problem and if you're only doing something the size of a watch, then it definitely shouldn't be a problem.
I hope this long (and quite possibly boring) post is of some help to you.
Regards
Warren