I've been making a lot of hammered wire jewelry lately. I'm kind of a DIY jewelry maker- not a professional at this point but I thought I would just chime in here in case it's at all helpful.
I've been working with copper wire from the hardware store. It's great to practice with when you're a beginner since it's inexpensive and easy to work with. I don't like how it looks when it's bright and shiny and new, but if you give it a dip in a liver of sulphur solution, let it dry, and buff the high points with fine steel wool it gets a beautiful warm vintage look that I really love.
I have a chasing hammer like this one http://www.amazon.com/10-CHASING-HAMMER-FORGED-HEAD/dp/B000E3277C that I bought for a silversmithing class. It's great for flattening & hardening wire and even making textures on metal.
I haven't gotten around to buying a steel bench block yet, but this would be good to hammer on http://www.jatayu.com/Merchant2/merchant.mvc?Screen=PROD&Store_Code=J&Product_Code=TAV-0100 I have a weird steel cylinder that my dad bought years ago, I think it is a giant truck piston... I hammer wire on the flat bottom of it. Any piece of flat steel will work. One of those little mini anvils that they sell at hardware stores could be lots of fun.
I also have a pair of round-nose pliers, wood dowels in various sizes, needle nose pliers, and wire cutters, and that's about all I need at this point.
I'm not sure about cleaning your watch parts. Maybe someone else will know.
Here's a bracelet I made recently
I made it without a wire jig or any fancy equipment.
Here are some links to free tutorials that I found helpful: http://www.jatayu.com/Education/Education.htm This bracelet was fun & easy to make: http://justsimplycharming.blogspot.com/2006/11/making-bracelet.html There are some good free wireworking tutorials here too: http://www.jewelrylessons.com/jewel/