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I would estimate $200-400 depending on which tools you already have and if you decide to print the case in plastic or metal.
The Ultimate Binary Watch
I used Chipquik SMD291AX which is Sn63/Pb37 solder paste. If you prefer lead-free paste I would suggest Sn42/Bi57/Ag01 for the WS2812B LEDs. I would try to avoid soldering these with a hot air gun if possible as heating them from the top has a tenancy to cause damage to these components. If possible use a reflow oven or a hot plate to do the soldering of these parts.